Gravitational wave complementarity and impact of NANOGrav data on gravitational leptogenesis: cosmic strings

In seesaw mechanism, if right handed (RH) neutrino masses are generated dynamically by a gauged $U(1)$ symmetry breaking, a stochastic gravitational wave background (SGWB) sourced by a cosmic string network could be a potential probe of leptogenesis. We show that the leptogenesis mechanism that facilitates the dominant production of lepton asymmetry via the quantum effects of right-handed neutrinos in gravitational background, can be probed by GW detectors as well as next-generation neutrinoless double beta decay ($0\nu\beta\beta$) experiments in a complementary way. We infer that for a successful leptogenesis, an exclusion limit on $f-\Omega_{\rm GW}h^2$ plane would correspond to an exclusion on the $|m_{\beta\beta}|-m_1$ plane as well. We consider a normal light neutrino mass ordering and discuss how recent NANOGrav pulsar timing data (if interpreted as GW signal) e.g., at 95$\%$ CL, would correlate with the potential discovery or null signal in $0\nu\beta\beta$ decay experiments.


1/AF Bidhannagar, Kolkata 700064, India
In seesaw mechanism, if right handed (RH) neutrino masses are generated dynamically by a gauged U (1) symmetry breaking, a stochastic gravitational wave background (SGWB) sourced by a cosmic string network could be a potential probe of leptogenesis. We show that the leptogenesis mechanism that facilitates the dominant production of lepton asymmetry via the quantum effects of right-handed neutrinos in gravitational background, can be probed by GW detectors as well as next-generation neutrinoless double beta decay (0νββ) experiments in a complementary way. We infer that for a successful leptogenesis, an exclusion limit on f − Ω GW h 2 plane would correspond to an exclusion on the |m ββ | − m 1 plane as well. We consider a normal light neutrino mass ordering and discuss how recent NANOGrav pulsar timing data (if interpreted as GW signal) e.g., at 95% CL, would correlate with the potential discovery or null signal in 0νββ decay experiments.
In the context of seesaw models and leptogenesis, one has a natural motivation for a spontaneous breaking of U (1) B−L [108,109] which generates heavy RH neutrino masses as well as gives a detectable cosmic string induced GW signal. This has been the central point of the studies in the Refs. [91,92]. We go in the same direction but consider RH neutrino induced gravitational leptogenesis mechanism (RIGL) [46] wherein lepton asymmetry is generated at two loop level due to the interactions of RH neutrinos with background gravity. A dynamical CPT violation in this process induces a lepton asymmetry in equilibrium which is maintained during the course of evolution until ∆L = 2 N 1 -interaction rates fall below the Hubble expansion rate. While even without flavour effects [110][111][112][113][114][115][116] in the washout processes, the mechanism is able to produce dominant lepton asymmetry (compared to the leptogenesis from decays) [43][44][45][46], when the effects are taken into account, the lightest RH mass scale M 1 can be lowered to M min ∼ 10 7 GeV [117] unlike the standard N 1 -thermal [118][119][120][121] leptogenesis scenario (T RH > M 1 ) where it is subjected to a lower bound of 10 9 GeV [122]. We consider a hierarchical spectrum of RH neutrinos assuming the heaviest mass scale is of the order of the U (1) breaking scale (Λ CS ) which also sets the initial temperature of asymmetry generation and masses of the other two are parametrically suppressed with the lightest being O(M min ). The magnitude of the final frozen out asymmetry depends on the heaviest mass scale as well as the strength of the ∆L = 2 N 1 -interactions which typically increase with the increase of the lightest light neutrino mass m 1 and cause a reduction in the magnitude of the final asymmetry. This opens up the possibility to probe the RIGL mechanism in GW detectors as well as absolute neutrino mass scale experiments and consequently neutrinoless double beta decay (0νββ) experiments. We show that a successful leptogenesis corresponds to Gµ > 4.4 × 10 −11 with a corresponding upper bound m 1 12 meV, where G is the Newton's constant and µ ∼ Λ 2 CS is the string tension. An increase in Gµ causes an increase in the upper bound on m 1 and hence less exclusion in the 0νββ decay parameter space. We then discuss the compatibility of RIGL mechanism with recent NANOGrav data and find that m 1 25 meV is disfavoured by NANOGrav at 2σ.
The rest of the paper is organised as follows: In sec.II we discuss the RIGL mechanism. In sec.III we briefly outline the production of GWs from cosmic string. In sec. IV we present the numerical analysis and an overall discussion. We summarise in sec.V.

II. RIGHT HANDED NEUTRINO INDUCED GRAVITATIONAL LEPTOGENESIS
The basic idea behind the gravitational leptogenesis [34] is that the C and CP violating operator L CP V ∼ b∂ µ Rj µ ∼ b∂ µ R¯ γ µ with b as a real effective coupling of mass dimension minus two, corresponds to a chemical potential µ = bṘ for the lepton number in the theory. Consequently, the normalised (by photon density n γ ∼ T 3 ) equilibrium lepton asymmetry which arises due to this chemical potential is given by N eq B−L ∼ bṘ T . Now an important question that can be addressed is, that without introducing the operator by hand, given a model, whether the operator can be generated dynamically. The authors of Refs. [43][44][45][46] showed that the Type-I seesaw mechanism which is otherwise studied for generating light neutrino masses and leptogenesis from RH neutrino decays [17], facilitates L CP V at two looplevel ( Fig.1) even when the seesaw Lagrangian is minimally coupled to the gravitational background. Physically, a non-vanishing value of the chemical potential which could be attributed to an asymmetric propagation of lepton and anti-lepton can be understood by computing the self energy diagrams for lepton and anti-lepton propagators (in gravitational background) which in the seesaw model leave different contributions only at the two loop level (Fig.1).
To understand how L CP V gets generated in seesaw model, one has to capitalise on the fact that the effective coupling 'b' is independent of the choice of background and therefore the computation can simply be done in a conformally flat metric given by so that the contribution from L CP V = b∂ µ R¯ γ µ to the effective h vertex in the momentum space reads where q = p − p is the momentum transfer between the ingoing (p ) and outgoing lepton(p) and the Ricci scalar is given by R = −3∂ 2 h. In the seesaw model, a construction of an effective h vertex that leaves a similar contribution as in Eq.II.2 would then manifest the generation L CP V operator. The coupling 'b' therefore can be calculated by matching the terms proportional to q 2 / q. Now looking at Fig.1, it is clear that to create an effective h vertex, one needs to have an insertion of h for example by the means of N N h, HHh, H N h etc. terms. Then the function A(q) can be calculated by computing the transition matrix element α (p )|Oh| α (p) , where the operator Oh can be generated using Eq.II.1 and a proper conformal rescaling [43,46]of the fields followed by an expansion (upto linear order in h)of UV Lagrangian where √ −g is the square root of the metric determinant, Lα = ν Lα e Lα T is the SM lepton doublet of flavour α,H = iσ 2 H * with H = H + H 0 T being the Higgs doublet and It can be shown that only the N N h insertion is what is relevant to the computation of the transition matrix element and essentially one has to compute four two-loop diagrams (two diagrams for each of the diagrams in Fig.1 with [44,46]. The contribution from these diagrams to the matrix element reads as where the loop function I [ij] depends on the heavy neutrino masses. Comparing Eq.II.2 and Eq.II.4, it is evident that the effective coupling b is simply given by and consequently, L CP V operator for one generation of leptons in seesaw model reads as Now recalling the chemical potential µ = bṘ, using standard Fermi-Dirac statistics for lepton and anti-lepton equilibrium densities and normalising the lepton asymmetry with photon number density, the net lepton asymmetry (summing over all the lepton generations) can be calculated as The general form of the loop function I [ij] is given by where p = 0, 1 [43][44][45][46]. Note that in Refs. [43][44][45][46], the authors show, though p = 0 is a conservative solution, p = 1 is also strongly preferred (see e.g., the discussion related to 'Diagram 4' in sec 4.1 of Ref. [44]. Briefly, the transition amplitude can be shown to be a difference between the amplitudes of two self-energy diagrams, where the first one shows a clear p = 1 behaviour and the second one which requires a non-trivial analytic computation of ten scalar topologies, from the power counting argument can be shown to be not dominant enough to cancel the amplitude of the first diagram. However, still there could be a room for an unlikely conspiracy for some of the scalar topologies of the second diagram to cancel the p = 1 behaviour of the first diagram. That fine-tuned region of parameter space requires full analytic computation of all the scalar topologies for the second diagram). Here we do not confront the robustness of p = 1 solution (or the 'hierarchically enhanced solution' [45,46]), rather we take it at face value. As an aside, let us mention that p = 0 solution does not work (cannot produce correct baryon asymmetry) in the standard cosmological evolution of the universe [45,46,117]. From now on we shall proceed with hierarchically enhanced equilibrium asymmetry considering a standard cosmological evolution and therefore, we stress that any conclusive future demurral of p = 1 would imply our analysis is invalid. To proceed further, the time derivative of the Ricci scalarṘ is given bẏ where σ = π 2 g * /30, M P l ∼ 2.4 × 10 18 GeV and ω being the equation of state parameter. A non-zero value ofṘ in radiation domination is obtained in all the usual scenarios of gravitational leptogenesis by considering so called trace-anomaly in the gauge sector allowing 1 − 3ω 0.1 1 [34]. The light neutrino masses are obtained from the flat space seesaw Lagrangian and are given in the flavour basis as where m D = f v with v = 174 GeV being the vacuum expectation value of the SM Higgs. Neutrino-less double beta decay parameter is the absolute value of the (11) element of M ν , i.e |M ν,11 | ≡ |m ββ | [123]. The mass matrix in Eq.II.12 can be diagonalised by a unitary matrix U as with m 1,2,3 being the physical light neutrino masses. We work in a basis where the RH neutrino mass matrix M R and charged lepton mass matrix m are diagonal. Therefore, the neutrino mixing matrix U can be written as where is an unphysical diagonal phase matrix and c ij ≡ cos θ ij , s ij ≡ sin θ ij with the mixing angles θ ij = [0, π/2]. Low energy CP violation enters in Eq. II.14 via the Dirac phase δ and the Majorana phases α M and β M . It is useful to parametrise (which can be straightforwardly derived from Eq.II.13) the Dirac mass matrix as [124] where Ω is a 3 × 3 complex orthogonal matrix and is given by where z ij = x ij + iy ij . In the hierarchical limit of the RH neutrinos M 3 M 2 M 1 , the equilibrium asymmetry can be approximated as As mentioned previously, one needs to compute the frozen out asymmetry N G0 B−L considering the effect of ∆L = 2 processes which tend to maintain the asymmetry N eq B−L in 1 Note that δω = 1 − 3ω 0.01 − 0.1 = 0 is a crucial ingredient of all the gravitational leptogenesis models.
In the SM, δω 0 is still a very good assumption at the higher temperatures [125]. Therefore, most of the gravitational leptogenesis models that assume a large and nonvanishing δω, intrinsically refer to a BSM theory. For example, without going into the detail of a specific BSM model, starting from the Ref. [34] to the Refs. [43][44][45][46] refer to δω ∼ 0.1 considering the finite temperature QCD as SU (N c ) gauge theory with N f massless quark flavours and coupling g which give rise to δω as [126] δω = 5 12π 2 so that typical gauge groups and matter content can easily yield δω 0.01 − 0.1 at high energy [34]. Note that we quote the result of Eq.3.88 of Ref. [125] which differs from the results of Eq.4 of Ref. [34] by a factor 2. equilibrium and therefore a dilution of the asymmetry from z in upto z 0 -the freeze-out point of the asymmetry. The asymmetry N G0 B−L can be obtained by solving a simple Boltzmann equation [46] where W ∆L=2 encodes the effect of ∆L = 2 process involving non-resonant N 1 -exchange and is given by [46,127] For a parametric scan using 3σ neutrino oscillation data [15], it is convenient to solve the BE in Eq.II.18 analytically. To this end, we re-write Eq.II.18 as and the unflavoured N 1 -decay parameter K 1 is given in terms of orthogonal matrix as The parameter Y which encodes the CP violation in the theory is given by Since the lightest RH scale is below 10 9 GeV, a second stage N 1 -washout by inverse decays occurs in all the three flavours and therefore the final asymmetry is given by [117] where the flavoured washout parameters are given by (II.26) One has to compare Eq.II.25 with the measured asymmetry at recombination In Fig.2, we show the dynamics of the lepton asymmetry production (inclusive of a second stage N 1 -washout for benchmark value of K 1α = 2). As one sees as κ increases ∆L = 2 interactions try to maintain the asymmetry in equilibrium for a longer period of time and hence causes a late freeze-out as well as a reduction in magnitude of the frozen out asymmetry. Thus, if the elements of the orthogonal matrix are not significantly large [128]which also correspond to a fine tuning in the seesaw formula [129,130], an increase of m 1 causes an increase of the value of κ (shown in Fig.3 ) and consequently the magnitude of the asymmetry reduces. This leads to an upper bound on m 1 for successful gravitational leptogenesis. Note that in the analytical formula for N f B−L we have neglected the flavour effect in the ∆L = 2 process as well as all the possible values of the flavour projectors (that project the asymmetry on the e, µ, τ basis) compatible with 3σ oscillation data. In Ref. [117] we computed it numerically and found these effects do not have any significant effect on the final asymmetry. For convenience, let us re-mention here that the frozen out asymmetry that is large enough in magnitude to be compatible with the observed one, corresponds to smaller values κ which are not very sensitive to the flavour effect. On the other hand, in the probability triangle, though flavour projectors show a biasness towards the electron flavour, P iα = 1/3 still remains a fair choice to take under consideration [117,129]. Therefore to efficiently scan the entire parameter space in the computer codes, we have simplified the final formula for N f B−L considering a democratic behaviour of the flavour projectors. A consideration of the full 3σ data for the flavour projectors (analytical formula including flavour projectors is given in Ref. [117]) would affect the final results only at the level of few percent. However, let us mention that in our previous analysis we did not take into account the effect of flavour-couplings (FC) at the N 1 -washout [111,116,[131][132][133]. Though in typical leptogenesis studies, FCs are included for more accurate computation involving flavour effect, in some scenarios, FCs play roles which are of great interest [116,133]. For example, in Ref. [116] it has been shown that even if CP violation is absent in one particular flavour, FCs can generate significant lepton asymmetry in that flavour. In this article we include the effect of FCs towards a fuller treatment of flavour effect and in the numerical section we shall state the percentage of correction to the final result. The flavour coupling effect is introduced in the washout equation as where P 1α = K 1α /K 1 and the flavour coupling matrices in the three flavour regime [116,132]  Clearly, unlike Eq.II.25 which is a solution of Eq.II.28 with C = I, now the equation for the final asymmetry would be more complicated and interestingly, a particular flavour component of the asymmetry would receive contribution from other flavours. For computational purpose, it is convenient to perform a basis rotation to make the Eq.II.28 diagonal in a redefined flavour basis. To this end, Eq.II.28 can be written in matrix form as where N ∆ = (N ∆e , N ∆µ , N ∆τ ) T andP 1 = P 1α C αβ . Introducing the V matrix that diago-nalisesP 1 as VP 1 V −1 =P 1 , Eq.II.31 can be written in the new flavour basis as where N ∆ = V N ∆ . Therefore, the asymmetry matrix in the prime is simply obtained as where K 1α = P 1α K 1 . Consequently, the final asymmetry matrix which we meed in the unprimed basis is obtained as Therefore, the total asymmetry that produces the observed baryon asymmetry is given by

III. GRAVITATIONAL WAVES FROM COSMIC STRING
Cosmic strings are natural prediction of many extension of standard model featuring U (1) symmetry breaking [73,74]. They are considered to be one dimensional object having string tension µ which is typically taken to be of the order of the square of the symmetry breaking scale. The normalised string tension Gµ, with G being the Newton's constant, is directly constrained by CMB as Gµ 1.1 × 10 −7 [134]. After formation, the strings are expected to reach a scaling regime in which their net energy density tracks the total energy density of the universe with a relative fraction Gµ. This regime is considered to have many closed loops and Hubble-length long strings which intersect to form new loops as the universe expands. All these loops oscillate and emit radiation, including gravitational waves. We consider stochastic gravitational background (SGWB) from cosmic string scaling by considering Nambu-goto strings which radiate energy dominantly in the form of GW radiation. We follow Ref. [79] to calculate SGWB from cosmic string. Once the loops are formed, they radiate energy in the form of gravitational radiation at a constant rate, mathematically described as where G is the usual gravitational constant and Γ = 50 [75,135]. Thus, the initial length l i = αt i of the loop decreases as until the loop disappears completely. The quantity α has a distribution and for the largest loop one typically has α = 0.1 [136,137] which we consider in the numerical calculation. The total energy loss from a loop is decomposed into a set of normal-mode oscillations at frequenciesf = 2k/l, where k = 1, 2, 3... The relic GW density parameter is given by where f is the red-shifted frequency and ρ c = 3H 2 0 /8πG. The GW density parameter Ω GW can be written as a sum over all relic densities corresponding to a mode k as where Ω (k) and the integration runs over the emission time with t F as time corresponding to the scaling regime of the loop after formation. The numerical values of C eff are found to be 5.7 and 0.5 at radiation and matter domination and F α has a value ∼ 0.1 [136,137]. The quantity t (k) i is the formation time of the loops contributing to the mode k and is given by The relative emission rate per mode is given by with ∞ m=1 m −4/3 3.6 and k Γ (k) = Γ. Having set up all the theoretical machineries, we now proceed towards the final discussion containing numerical results.

IV. NUMERICAL RESULTS AND DISCUSSIONS
To generate all the plots in Fig.3, we scanned over 3σ neutrino oscillation data [15] and used the seesaw fine-tuning parameter γ i = j |Ω 2 ij | 1 which also helps to avoid the non-perturbative Yukawa couplings, i.e., Tr(f † f ) ≤ 4π. We use the upper bound on the sum of the light neutrino masses as i m i < 0.17 eV [1] which corresponds to m 1 50 meV as shown by vertical light blue shade in each of the plots. A more stringent upper bound m 1 31 meV is also available from latest PLANCK data [2,139]. The red vertical region is the future sensitivity region of the KATRIN experiment which is starting to measure neutrino masses with an ultimate sensitivity to 0.2 eV [138]. In the top panel of the figure, we show the variation of κ with m 1 which indicates that for m 1 10 −2 eV, κ increases rapidly. An immediate consequence can be seen in the middle panel where N B−L has a decreasing slope for m 1 10 −2 eV. This corresponds to the previously mentioned late freeze out solutions as also shown in Fig.2. We show three gray shaded exclusion regions for the string tensions Gµ = 4.44 × 10 −11 , 2.7 × 10 −10 and 1.7 × 10 −9 which correspond to the upper bounds m 1 10 meV, 21 meV and 31 meV for successful leptogenesis. Corresponding exclusion regions on the effective matrix element of 0νββ decay have been shown in the bottom panel. The horizontal gray shaded region represents the already excluded region and the yellow shaded region represents the future sensitivity limits of next-generation 0νββ experiments. A comprehensive discussion about all the current and planned 0νββ experiments can be found in Ref. [138]. The above numerical discussion excludes the contribution of the FCs since it is sufficient to consider Eq.II.25 to have an overall idea of the parameter space. However, to obtain more accurate upper bounds, it is instructive to include FCs as discussed in sec.II. Using Eq.II.35 with a democratic behaviour of the flavour projectors, we perform a full numerical scan of the parameter space and find bit more relaxed upper bounds on m 1 . For the mentioned values of Gµ, we find m 1 12 meV, 25 meV and 36 meV for successful leptogenesis. This implies in this scenario, FCs give correction around 17% − 20% to the final result. We would like to take this opportunity to mention that we expect some level of correction to the parameter space (which does not include FCs) in our previous publication [117] as well, where we discuss the flavour effects in RIGL mainly focusing on a two-RH neutrino scenario. A complete discussion in this context will be presented elsewhere.
As one notices on the middle panel, a decrease in the string tension results in a decrease in the magnitude of the overall asymmetry which goes below the observed value (N Obs B−L ) for Gµ < 4.4 × 10 −11 . Therefore, RIGL will be fully tested in the space-based interferometers such as LISA [140], Taiji [141], TianQin [142], BBO [143], DECIGO [144], ground based interferometers like Einstein Telescope (ET) [145] and Cosmic Explorer (CE) [146], and atomic interferometers MAGIS [147], AEDGE [148] over wide range of frequencies. Of course, as already argued, any exclusion of the string tension value Gµ > 4.4 × 10 −11 by the GW detectors would put an exclusion region in the |m ββ | parameter space or future discovery of 0νββ signal for m 1 > 10 meV would put a lower bound on the string tension that would be tested by the GW detectors. In the left panel of Fig.4, we show the GW spectrum that corresponds to an upper bound on m 1 within the range 12 meV-36 meV (bottom-up). We now conclude the paper by analysing the recent NANOGrav pulsar timing array (PTA) data which if interpreted as GW signal, would put an interesting constraint on RIGL mechanism.
Though the idea of detecting GW with PTA is very much well known, for completeness we write few sentences. Pulsars are highly magnetised and rapidly rotating neutron stars. They emit radio waves from their magnetic poles and we observe these waves on the Earth as a string of pulses. Since neutron stars are of high densities, the time of arrival (TOA) of pulses are highly regular and that is why they are used in high precision timing experiments. Millisecond pulsars (spins ∼ 100 times a second) produce most stable pulses and are used by the PTAs. When a "disturbance" like gravitational wave passes through the earth and pulsar system, the time of arrival of the signal from the pulsars changes. This induces a frequency change in the pulses (contributes to a measurable quantity called time residual R ∝ δν ν ). The NANOGrav collaboration with their recently released data reports a strong evidence for a stochastic common-spectrum process (they analysed 45 pulsars) over independent-red noises [93]. However, they do not claim the detection as GW, since the time residuals do not show characteristic spatial relation described by the Hellings-Downs (HD) curve [149]. In addition, other systematics such as pulsar spin noise [150] and solar system effects [151] might affect the signal thus the analysis requires proper handling of these two effects-a study which is in preparation [93]. In any case, if in the near future, more data and a more rigorous statistical analysis by NANOGrav leads to the detection to SGWB, it would undoubtedly open up a new direction to probe Early Universe cosmology. This of course includes leptogenesis as well. Remarkably enough, testing leptogenesis with pulsars would be a completely novel aspect which can serve also as a complementary probe of leptogenesis alongside the experiments in the particle physics side such as neutrino oscillation and neutrino-less double beta decay [55,59]. Let us now focus on the analysis of gravitational leptogenesis scenario with respect to the NANOGrav data. The 12.5 yrs NANOGrav data are expressed in terms of power-law signal with characteristic strain given by with f yr = 1yr −1 and A being the characteristic strain amplitude. The abundance of GWs has the standard form and can be recast as: We do a simple power law fit to the cosmic string generated GW spectra using Eq.IV.2 and show the results in the right panel of Fig.4 on the spectral index (γ)-amplitude (A) plane against the NANOGrav@1σ and 2σ contours. We plot the same benchmark values of Gµ that were used in Fig.3, i.e., Gµ = 4.44 × 10 −11 , 2.7 × 10 −10 and 1.7 × 10 −9 . These values are plotted as solid red circle, square and diamond points. We find Gµ = 2.7 × 10 −10 is at the edge of the 2σ. Thus RIGL disfavours m 1 > 25 meV at NANOGrav@2σ. Let's point out that our fit is consistent with Ref. [94], e.g., Gµ ∼ 2.7 × 10 −10 is disfavored at 2σ, however, we get the strain amplitude value slightly lower than Ref. [94]. The new NANOGrav 12.5 yr data [93] though consistent with previous EPTA data [152], they are in tension with previous limits from PPTA [153] and a previous NANOGrav analysis of their 11 yr data [154]. This tension would be reduced using improved prior to the intrinsic pulsar red noise to the older data [93].

V. SUMMARY
We analyse a cosmic string induced GW spectrum as a test of leptogenesis. We discuss gravitational leptogenesis within the Type-1 seesaw which is otherwise studied in general for leptogenesis from right handed neutrino decays. An operator of the form L CP V ∼ b∂ µ Rj µ ∼ b∂ µ R¯ γ µ can generate a lepton asymmetry N B−L ∼ bṘ T in thermal equilibrium evading Sakharov's third condition for baryogenesis. In seesaw model L CP V can be created at two loop level with the right handed neutrinos as virtual particles. The generated equilibrium asymmetry is maintained (decreases with temperature) until the non-resonant ∆L = 2 N 1 -interaction goes out of equilibrium (then the asymmetry freezes out). The magnitude of the final asymmetry which depends on the lightest light neutrino mass m 1 , typically decreases with the m 1 and therefore the parameter space of the leptogenesis is sensitive to m 1 as well as the neutrino less double beta decay parameter |m 11 |, through m 1 . We consider that the masses of the right handed neutrinos are generated dynamically by an U (1) B−L symmetry breaking which also leads to a formation of cosmic string network that produce gravitational waves. Therefore, the mechanism is sensitive to gravitational wave physics as well as low energy neutrino physics. We show that right handed neutrino induced gravitational leptogenesis can be probed by the gravitational wave detectors as well as next-generation neutrinoless double beta decay experiments in a complementary manner such that an exclusion limit on f − Ω GW h 2 plane would correspond to an exclusion on the |m ββ | − m 1 plane as well. We consider a normal light neutrino mass ordering and show that the gravitational wave detectors can fully test the mechanism for a wide range of frequencies.
We then show that recent NANOGrav pulsar timing data (if interpreted as GW signal) would exclude 0νββ parameter space for m 1 25 meV at ∼ 2σ.