Skip to main content
SpringerLink
Log in

Cosmological Inflation Based on the Uncertainty-Mediated Dark Energy

  • Published:
Gravitation and Cosmology Aims and scope Submit manuscript

Abstract

It was suggested in our previous paper [Yu.V. Dumin, Grav. Cosmol. 25, 169 (2019)] that the cosmological Dark Energy might be mediated by the time–energy uncertainty relation in the Mandelstam–Tamm form, which is appropriate for the long-term evolution of quantum systems. The amount of such Dark Energy gradually decays with time, and the corresponding scale factor of the Universe increases by a “quasi-exponential” law (namely, the exponent is proportional to of the square root of time) throughout the entire cosmological evolution. While such a universal behavior looks quite appealing, an important question arises: Does the quasi-exponential expansion resolve the major problems of the early Universe in the same way as the standard inflationary scenario? In the present paper, we elucidate this issue by analyzing the causal structure of the space–time following from this model. It is found that the observed region of the Universe (the past light cone) covers a single causally connected domain developing from the Planck times (the future light cone). Consequently, there should be no appreciable inhomogeneity and anisotropy in the early Universe, creation of the topological defects will be suppressed, etc. From this point of view, the uncertainty-mediated Dark Energy can serve as a reasonable alternative to the standard (exponential) inflationary scenario.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3

Similar content being viewed by others

Notes

  1. Some qualitative conjectures about a possible role of the uncertainty relation for the explanation of Dark Energy were put forward by Coe in [4], but the quantitative analysis performed there looks absolutely unreasonable.

  2. From the mathematical point of view, this differential equation is non-autonomous, i.e., involves the explicit dependence on time, which is quite an unusual situation in cosmology. However, as follows from the subsequent analysis, this fact does not result in any substantial peculiarities of the solution: it turns out to be well between the solutions of usual cosmological equations obtained under various assumptions.

  3. We prefer to not call it the Big Bang, because in modern literature this term often refers to the onset of the “hot” stage, when ordinary matter becomes dominant.

  4. In principle, our equations might be favorable for constructing a bounce-type model of the Universe, but we prefer not to speculate about processes at Planckian times.

REFERENCES

  1. Yu. V. Dumin, “A unified model of Dark Energy based on the Mandelstam–Tamm uncertainty relation,” Grav. Cosmol. 25, 169 (2019).

    Article  ADS  MathSciNet  Google Scholar 

  2. L. I. Mandelstam and I. E. Tamm, “The energy–time uncertainty relation in nonrelativistic quantum mechanics,” Izv. Akad. Nauk SSSR (Ser. Fiz.) 9, 122 (1945), in Russian.

    Google Scholar 

  3. S. Deffner and S. Campbell, “Quantum speed limits: from Heisenberg’s uncertainty principle to optimal quantum control,” J. Phys. A: Math. Theor. 50, 453001 (2017).

    Article  ADS  MathSciNet  Google Scholar 

  4. A. Coe, “Observable Universe topology and Heisenberg uncertainty principle,” Preprint viXra: 1710.0143.

  5. K. A. Olive and J. A. Peacock, “Big-Bang cosmology,” in: C. Patrignani et al. (Particle Data Group), Review of Particle Physics, Chin. Phys. C 40, 355 (2016).

  6. M. J. Mortonson, D. H. Weinberg, and M. White, “Dark Energy,” in: C. Patrignani, et al. (Particle Data Group), Review of Particle Physics, Chin. Phys. C 40, 402 (2016).

  7. J. Martin, C. Ringeval, and V. Vennin, “Encyclopaedia inflationaris,” Phys. Dark Universe 5-6, 75 (2014).

    Article  ADS  Google Scholar 

  8. J. Ellis and D. Wands, “Inflation,” in: C. Patrignani, et al. (Particle Data Group), Review of Particle Physics, Chin. Phys. C 40, 367 (2016).

  9. A. H. Guth, “The inflationary Universe: A possible solution to the horizon and flatness problems,” Phys. Rev. D 23, 347 (1981).

    Article  ADS  Google Scholar 

  10. A. D. Linde, “The inflationary Universe,” Rep. Prog. Phys. 47, 925 (1984).

    Article  ADS  MathSciNet  Google Scholar 

  11. A. A. Starobinsky, “A new type of isotropic cosmological models without singularity,” Phys. Lett. B 91, 99 (1980).

    Article  ADS  Google Scholar 

  12. A. D. Sakharov, “Vacuum quantum fluctuations in curved space and the theory of gravitation,” Dokl. Akad. Nauk SSSR 177, 70 (1967), in Russian.

    ADS  MathSciNet  Google Scholar 

  13. C. W. Misner, “Mixmaster Universe,” Phys. Rev. Lett. 22, 1071 (1969).

    Article  ADS  Google Scholar 

  14. N. N. Bogoliubov, “Field-theoretical methods in physics,” Suppl. Nuovo Cimento (Ser. prima) 4, 346 (1966).

  15. Ia. B. Zeldovich, I. Yu. Kobzarev, and L. B. Okun, “Cosmological consequences of a spontaneous breakdown of a discrete symmetry,” Sov. Phys. JETP 40, 1 (1975).

    ADS  Google Scholar 

  16. T. W. B. Kibble, “Topology of cosmic domains and strings,” J. Phys. A: Math. Gen. 9, 1387 (1976).

    Article  ADS  Google Scholar 

  17. W. H. Zurek, “Cosmological experiments in superfluid helium?” Nature 317, 505 (1985).

    Article  ADS  Google Scholar 

  18. H. V. Klapdor-Kleingrothaus and K. Zuber, Particle Astrophysics (Inst. Phys. Publ., Bristol, 1997).

    MATH  Google Scholar 

Download references

ACKNOWLEDGMENTS

I am grateful to A. Starobinsky, J.-P. Uzan, C. Wetterich, C. Kiefer and the members of his group for valuable discussions and critical comments.

Author information

Authors and Affiliations

  1. Space Research Institute (IKI), Russian Academy of Sciences, Profsoyuznaya str. 84/32, Moscow, 117997, Russia

    Yu. V. Dumin

  2. Sternberg Astronomical Institute (GAISh), Lomonosov Moscow State University, Universitetskii prosp. 13, Moscow, 119234, Russia

    Yu. V. Dumin

Authors
  1. Yu. V. Dumin
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Yu. V. Dumin.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Dumin, Y.V. Cosmological Inflation Based on the Uncertainty-Mediated Dark Energy. Gravit. Cosmol. 26, 259–264 (2020). https://doi.org/10.1134/S0202289320030068

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S0202289320030068

Search

Navigation