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Erratum to: Thermodynamic implications of the gravitationally induced particle creation scenario

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1 Erratum to: Eur. Phys. J. C (2017) 77:196  https://doi.org/10.1140/epjc/s10052-017-4746-4

We would like to rectify an error regarding the validity of the first law of thermodynamics (FLT) on the apparent horizon of a spatially flat Friedmann–Lemaitre–Robertson–Walker (FLRW) universe for the gravitationally induced particle creation scenario with constant specific entropy and an arbitrary particle creation rate \(\Gamma \) (see Sect. 3.1 of original article). Please note that the subsequent calculations in the original article are not affected in any way by this unfortunate error.

Now, in Eq. (14), the differential \(dE_A\) of the amount of energy crossing the apparent horizon will be
$$\begin{aligned} -\mathrm{d}E_A= & {} \frac{1}{2}R_{A}^{3}(\rho +p+\Pi )H\mathrm{d}t \\= & {} \frac{3\gamma }{2}\left( 1-\frac{\Gamma }{3H}\right) \mathrm{d}t. \end{aligned}$$
and NOT
$$\begin{aligned} -\mathrm{d}E_A= & {} \frac{1}{2}R_{A}^{3}(\rho +p)H\mathrm{d}t \\= & {} \frac{3\gamma }{2}\mathrm{d}t, \end{aligned}$$
as we had previously calculated. The FLT, which was not true in general in our original work, now clearly holds and this puts our model on a stronger footing since the FLT, being an energy conservation law, should always hold good in a perfect thermodynamic system.

Thus, in this erratum, we clarify that the FLT is always true on the apparent horizon of a spatially flat FLRW universe for the gravitationally induced particle creation scenario with constant specific entropy and an arbitrary particle creation rate.

Notes

Acknowledgements

Subhajit Saha was supported by SERB, Govt.of India under National Post-doctoral Fellowship Scheme [File No. PDF/2015/000906]. Anindita Mondal wishes to thank DST, Govt. of India for providing Senior Research Fellowship.

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© The Author(s) 2018

Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

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Authors and Affiliations

  1. 1.Department of Physical SciencesIndian Institute of Science Education and Research KolkataMohanpurIndia
  2. 2.Department of Astrophysics and CosmologyS N Bose National Centre for Basic SciencesKolkataIndia

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