Abstract
Scalar-tensor theory of gravity with non-minimal coupling is a fairly good candidate for dark energy, required to explain late-time cosmic evolution. Here we study the very early stage of evolution of the universe with a modified version of the theory, which includes scalar curvature squared term. One of the key aspects of the present study is that, the quantum dynamics of the action under consideration ends up generically with de-Sitter expansion under semiclassical approximation, rather than power-law. This justifies the analysis of inflationary regime with de-Sitter expansion. The other key aspect is that, while studying gravitational perturbation, the perturbed generalized scalar field equation obtained from the perturbed action, when matched with the perturbed form of the background scalar field equation, relates the coupling parameter and the potential exactly in the same manner as the solution of classical field equations does, assuming de-Sitter expansion. The study also reveals that the quantum theory is well behaved, inflationary parameters fall well within the observational limit and quantum perturbation analysis shows that the power-spectrum does not deviate considerably from the standard one obtained from minimally coupled theory.
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References
J.-P. Uzan, Cosmological scaling solutions of nonminimally coupled scalar fields, Phys. Rev. D 59 (1999) 123510 [gr-qc/9903004] [INSPIRE].
L. Amendola, Coupled quintessence, Phys. Rev. D 62 (2000) 043511 [astro-ph/9908023] [INSPIRE].
R. Bean and J. Magueijo, Dilaton derived quintessence scenario leading naturally to the late time acceleration of the universe, Phys. Lett. B 517 (2001) 177 [astro-ph/0007199] [INSPIRE].
R. Bean, Perturbation evolution with a nonminimally coupled scalar field, Phys. Rev. D 64 (2001) 123516 [astro-ph/0104464] [INSPIRE].
B. Boisseau, G. Esposito-Farese, D. Polarski and A.A. Starobinsky, Reconstruction of a scalar tensor theory of gravity in an accelerating universe, Phys. Rev. Lett. 85 (2000) 2236 [gr-qc/0001066] [INSPIRE].
N. Agarwal and R. Bean, The Dynamical viability of scalar-tensor gravity theories, Class. Quant. Grav. 25 (2008) 165001 [arXiv:0708.3967] [INSPIRE].
A. Cid, G. Leon and Y. Leyva, Intermediate accelerated solutions as generic late-time attractors in a modified Jordan-Brans-Dicke theory, JCAP 02 (2016) 027 [arXiv:1506.00186] [INSPIRE].
N. Bartolo and M. Pietroni, Scalar tensor gravity and quintessence, Phys. Rev. D 61 (2000) 023518 [hep-ph/9908521] [INSPIRE].
D.J. Holden and D. Wands, Selfsimilar cosmological solutions with a nonminimally coupled scalar field, Phys. Rev. D 61 (2000) 043506 [gr-qc/9908026] [INSPIRE].
G. Leon, On the Past Asymptotic Dynamics of Non-minimally Coupled Dark Energy, Class. Quant. Grav. 26 (2009) 035008 [arXiv:0812.1013] [INSPIRE].
K. Nozari and S.D. Sadatian, Late-time acceleration and Phantom Divide Line Crossing with Non-minimal Coupling and Lorentz Invariance Violation, Eur. Phys. J. C 58 (2008) 499 [arXiv:0809.4744] [INSPIRE].
L.N. Granda, Cosmological Dynamics of Scalar Field with Non-Minimal Coupling to Gravity, Rev. Col. Fís. 42 (2010) 63.
K.S. Stelle, Renormalization of Higher Derivative Quantum Gravity, Phys. Rev. D 16 (1977) 953 [INSPIRE].
B. Tajahmad and A.K. Sanyal, Unified cosmology with scalar-tensor theory of gravity, Eur. Phys. J. C 77 (2017) 217 [arXiv:1612.04239] [INSPIRE].
A.A. Starobinsky, A New Type of Isotropic Cosmological Models Without Singularity, Phys. Lett. B 91 (1980) 99 [INSPIRE].
K.-i. Maeda, Inflation as a Transient Attractor in R 2 Cosmology, Phys. Rev. D 37 (1988) 858 [INSPIRE].
E.T. Whittaker, A treatise on the analytical dynamics of particles and rigid bodies, Cambridge University Press (1904).
P.A.M. Dirac, Generalized Hamiltonian dynamics, Can. J. Math. 2 (1950) 129 [INSPIRE].
P.A.M. Dirac, Lectures on Quantum Mechanics, Belfer Graduate School of Science, Yeshiva University, New York (1964).
G.T. Horowitz, Quantum Cosmology With a Positive Definite Action, Phys. Rev. D 31 (1985) 1169 [INSPIRE].
A.K. Sanyal and B. Modak, Quantum cosmology with a curvature squared action, Phys. Rev. D 63 (2001) 064021 [gr-qc/0107001] [INSPIRE].
A.K. Sanyal and B. Modak, Quantum cosmology with R + R 2 gravity, Class. Quant. Grav. 19 (2002) 515 [gr-qc/0107070] [INSPIRE].
A.K. Sanyal, Quantum mechanical probability interpretation in the minisuperspace model of higher order gravity theory, Phys. Lett. B 542 (2002) 147 [gr-qc/0205053] [INSPIRE].
A.K. Sanyal, Quantum mechanical formulation of quantum cosmology for brane world effective action, gr-qc/0305042 [INSPIRE].
A.K. Sanyal, Hamiltonian formulation of curvature squared action, Gen. Rel. Grav. 37 (2005) 1957 [hep-th/0407141] [INSPIRE].
A.K. Sanyal, S. Debnath and S. Ruz, Canonical formulation of curvature squared action in the presence of lapse function, Class. Quant. Grav. 29 (2012) 215007 [arXiv:1108.5869] [INSPIRE].
S. Debnath, S. Ruz and A.K. Sanyal, Canonical formulation of scalar curvature squared action in higher dimensions, Phys. Rev. D 90 (2014) 047504 [arXiv:1408.1765] [INSPIRE].
K. Sarkar, N. Sk, R. Mandal and A.K. Sanyal, Canonical formulation of Pais-Uhlenbeck action and resolving the issue of branched Hamiltonian, Int. J. Geom. Meth. Mod. Phys. 14 (2016) 1750038 [arXiv:1507.03444] [INSPIRE].
S. Ruz, R. Mandal, S. Debnath and A.K. Sanyal, Resolving the issue of branched Hamiltonian in modified Lanczos-Lovelock gravity, Gen. Rel. Grav. 48 (2016) 86 [arXiv:1409.7197] [INSPIRE].
R. Mandal and A. Kumar Sanyal, Equivalent and inequivalent canonical structures of higher order theories of gravity, Phys. Rev. D 96 (2017) 084025 [arXiv:1709.05201] [INSPIRE].
J.W. York Jr., Role of conformal three geometry in the dynamics of gravitation, Phys. Rev. Lett. 28 (1972) 1082 [INSPIRE].
G.W. Gibbons and S.W. Hawking, Action Integrals and Partition Functions in Quantum Gravity, Phys. Rev. D 15 (1977) 2752 [INSPIRE].
E. Dyer and K. Hinterbichler, Boundary Terms, Variational Principles and Higher Derivative Modified Gravity, Phys. Rev. D 79 (2009) 024028 [arXiv:0809.4033] [INSPIRE].
V. Iyer and R.M. Wald, A Comparison of Noether charge and Euclidean methods for computing the entropy of stationary black holes, Phys. Rev. D 52 (1995) 4430 [gr-qc/9503052] [INSPIRE].
F. Briscese and E. Elizalde, Black hole entropy in modified gravity models, Phys. Rev. D 77 (2008) 044009 [arXiv:0708.0432] [INSPIRE].
J.C. Hwang, Cosmological perturbations in generalized gravity theories: Formulation, Class. Quant. Grav. 7 (1990) 1613 [INSPIRE].
J.-c. Hwang, Cosmological perturbations in generalized gravity theories: Conformal transformation, Class. Quant. Grav. 14 (1997) 1981 [gr-qc/9605024] [INSPIRE].
M. Satoh, S. Kanno and J. Soda, Circular Polarization of Primordial Gravitational Waves in String-inspired Inflationary Cosmology, Phys. Rev. D 77 (2008) 023526 [arXiv:0706.3585] [INSPIRE].
D.J. Schwarz, C.A. Terrero-Escalante and A.A. Garcia, Higher order corrections to primordial spectra from cosmological inflation, Phys. Lett. B 517 (2001) 243 [astro-ph/0106020] [INSPIRE].
S.M. Leach, A.R. Liddle, J. Martin and D.J. Schwarz, Cosmological parameter estimation and the inflationary cosmology, Phys. Rev. D 66 (2002) 023515 [astro-ph/0202094] [INSPIRE].
D.J. Schwarz and C.A. Terrero-Escalante, Primordial fluctuations and cosmological inflation after WMAP 1.0, JCAP 08 (2004) 003 [hep-ph/0403129] [INSPIRE].
M. Satoh and J. Soda, Higher Curvature Corrections to Primordial Fluctuations in Slow-roll Inflation, JCAP 09 (2008) 019 [arXiv:0806.4594] [INSPIRE].
J.C. Hwang, Curved space quantum scalar field theory with accompanying metric fluctuations, Phys. Rev. D 48 (1993) 3544 [INSPIRE].
J.C. Hwang, Perturbative semiclassical approximation in the uniform curvature gauge, Class. Quant. Grav. 11 (1994) 2305 [INSPIRE].
J.-c. Hwang, Quantum fluctuations of cosmological perturbations in generalized gravity, Class. Quant. Grav. 14 (1997) 3327 [gr-qc/9607059] [INSPIRE].
J.-c. Hwang, Unified analysis of cosmological perturbations in generalized gravity, Phys. Rev. D 53 (1996) 762 [gr-qc/9509044] [INSPIRE].
J.-c. Hwang and H. Noh, Cosmological perturbations in generalized gravity theories, Phys. Rev. D 54 (1996) 1460 [INSPIRE].
J.-c. Hwang and H. Noh, Density spectra from pole-like inflations based on generalized gravity theories, Class. Quant. Grav. 15 (1998) 1387.
H. Noh, Cosmological Perturbations in Generalized Gravity Theories Including Tachyon, in proceedings of 22nd Texas Symposium on Relativistic Astrophysics at Stanford University, December 13-17, 2004.
V.F. Mukhanov, Quantum Theory of Gauge Invariant Cosmological Perturbations, Sov. Phys. JETP 67 (1988) 1297 [INSPIRE].
J. Martin and D.J. Schwarz, New exact solutions for inflationary cosmological perturbations, Phys. Lett. B 500 (2001) 1 [astro-ph/0005542] [INSPIRE].
E.D. Stewart and D.H. Lyth, A More accurate analytic calculation of the spectrum of cosmological perturbations produced during inflation, Phys. Lett. B 302 (1993) 171 [gr-qc/9302019] [INSPIRE].
T.T. Nakamura and E.D. Stewart, The Spectrum of cosmological perturbations produced by a multicomponent inflaton to second order in the slow roll approximation, Phys. Lett. B 381 (1996) 413 [astro-ph/9604103] [INSPIRE].
Planck collaboration, P.A.R. Ade et al., Planck 2015 results. XX. Constraints on inflation, Astron. Astrophys. 594 (2016) A20 [arXiv:1502.02114] [INSPIRE].
F.J. de Urries and J. Julve, Ostrogradski formalism for higher derivative scalar field theories, J. Phys. A 31 (1998) 6949 [hep-th/9802115] [INSPIRE].
L. Querella, Variational principles and cosmological models in higher order gravity, Ph.D. Thesis, Université de Liege (1998) [gr-qc/9902044] [INSPIRE].
D.G. Boulware, Quantum Theory of Gravity, S.M. Christensen ed., Adam Hilger Ltd. (1984).
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Mandal, R., Sarkar, C. & Sanyal, A.K. Early universe with modified scalar-tensor theory of gravity. J. High Energ. Phys. 2018, 78 (2018). https://doi.org/10.1007/JHEP05(2018)078
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DOI: https://doi.org/10.1007/JHEP05(2018)078