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Zeitschrift für Naturforschung A

A Journal of Physical Sciences

Editor-in-Chief: Holthaus, Martin

Editorial Board: Fetecau, Corina / Kiefer, Claus

IMPACT FACTOR 2016: 1.432

CiteScore 2017: 1.30

SCImago Journal Rank (SJR) 2017: 0.403
Source Normalized Impact per Paper (SNIP) 2017: 0.632

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Volume 74, Issue 2


Modeling Cosmic Expansion, and Possible Inflation, as a Thermodynamic Heat Engine

Christopher Pilot
Published Online: 2018-12-04 | DOI: https://doi.org/10.1515/zna-2018-0314


Assuming a closed universe with slight positive curvature, cosmic expansion can be modeled as a heat engine where we define the “system,” collectively, as those regions of space within the observable universe, which will later evolve into voids. We identify the “surroundings,” collectively, as those pockets of space that will eventually develop into matter-filled galaxies, clusters, superclusters, and filament walls. Using this model, we can find the energy needed for cosmic expansion using basic thermodynamic principles and show that cosmic expansion had as its origin a finite initial energy density, pressure, volume, and temperature. Inflation in the traditional sense, with the inflaton field, may also not be required. We also argue that homogeneities and inhomogeneities in the WMAP temperature profile are attributable to quantum mechanical fluctuations about a fixed background temperature in the initial isothermal expansion phase of the cycle, which we identify with inflation. Fluctuations in temperature can cause certain regions of space to lose heat while other regions will absorb that heat. The voids, being those regions that absorb the heat, will expand, thereby leaving slightly cooler temperatures for the surroundings, where matter will later congregate. Upon freeze-out, this could produce the observed WMAP signature with its associated inhomogeneity. Finally, using the uncertainty relation, we estimate that the temperature and time for formation of WMAP inhomogeneities occurred at roughly 3.02 × 1027 K and 2.54 × 10−35 s, respectively, after first initiation of volume expansion. This is in line with current estimates for the end of the inflationary epoch. The heat input in the inflationary phase is calculated as roughly Q = 1.81 × 1094 J (photons only); the collective void volume increases by a factor of only 5.65. The bubble voids in the observable universe increase in size from about 0.046 to 0.262 m3 within this inflationary period in our model.

Keywords: Cosmic Evolution; Cosmological Expansion; Heat Engine; Isothermal Inflation Model; Thermodynamic Inflation


  • [1]

    J. L. Tonry, B. P. Schmidt, B. Barris, P. Candia, P. Challis, et al., Astrophys. J. 594, 1 (2003).CrossrefGoogle Scholar

  • [2]

    E. Komatsu, K. M. Smith, J. Dunkley, C. L. Bennett, B. Gold, et al., Astrophys. J. Suppl. S. 192, 18 (2011).CrossrefGoogle Scholar

  • [3]

    C. L. Bennett, D. Larson, J. L. Weiland, N. Jarosik, G. Hinshaw, et al., Astrophys. J. Suppl. S. 208, 20 (2013).CrossrefGoogle Scholar

  • [4]

    P. A. R. Ade, N. Aghanim, C. Armitage-Caplan, M. Arnaud, et al., Planck 2015 results. XIII. Cosmological parameters. Astronomy and Astrophysics (A&A) Volume 594 (Oct. 2016) A13 arXiv preprint 1502.1589v2[1] 6 Feb 2015. The value quoted is Ωk = −.005+.016–.017 (95% Planck TT + low P + lensing). See section 6.2.4 on curvature, in particular, equation (49).Google Scholar

  • [5]

    A. Einstein, Sitz Preuss Akad. d. Wiss Phys.-Math, 142 (1917).Google Scholar

  • [6]

    J. A. Wheeler, Einstein’s Vision, Springer, Berlin 1968.Google Scholar

  • [7]

    A. H. Guth, Phys. Rev. D 23, 347 (1981).CrossrefGoogle Scholar

  • [8]

    A. D. Linde, Phys. Lett. B 129, 177 (1983).CrossrefGoogle Scholar

  • [9]

    A. D. Linde, Phys. Rev. D 49, 748 (1994). This article gives a classification of inflation models.Google Scholar

  • [10]

    J. D. Barrow and W. S. Hawthorne, Mon. Not. R. Astr. Soc 243, 608 (1990).Google Scholar

  • [11]

    B. Ryden, Introduction to Cosmology, Addison Wesley, San Francisco, CA 2006.Google Scholar

  • [12]

    V. Mukhanov, Physical Foundations of Cosmology, Cambridge University Press, Cambridge, UK 2005.Google Scholar

  • [13]

    R. Brandenberger, PoS (ICFI 2010) 001 arXiv:1103.2271 [astro-ph.CO].Google Scholar

  • [14]

    J. Gonzalez-Ayala, J. Perez-Oregon, R. Cordero, and F. Angulo-Brown, Entropy 17, 4563 (2015).CrossrefGoogle Scholar

  • [15]

    J. Gonzalez-Ayala, R. Cordero, and F. Angulo-Brown, EPL (Europhysics Letters) 113, 4006 (2016).Google Scholar

  • [16]

    P. T. Landsberg and A. De Vos. J. Phys. A-Math. Gen. 22, 1073 (1989).CrossrefGoogle Scholar

  • [17]

    V. J. Menon and D. C. Agrawal, J. Phys. A-Math. Gen. 31, 1109 (1998).CrossrefGoogle Scholar

  • [18]

    I. Bars and J. Terning, Extra Dimensions in Space and Time, Springer, Berlin 2009.Google Scholar

  • [19]

    C. Lineweaver and T. M. Davis, Sci. Am. 292, 24 (2005).Google Scholar

About the article

Received: 2018-06-28

Accepted: 2018-10-21

Published Online: 2018-12-04

Published in Print: 2019-01-28

Citation Information: Zeitschrift für Naturforschung A, Volume 74, Issue 2, Pages 153–162, ISSN (Online) 1865-7109, ISSN (Print) 0932-0784, DOI: https://doi.org/10.1515/zna-2018-0314.

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