Generation of CMB and cosmological constant via bulk viscosity
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Generation of CMB and cosmological constant via bulk viscosity Sanved Kolekar1
· S. Shankaranarayanan2
· S. M. Chitre1
Received: 18 May 2020 / Accepted: 16 September 2020 © Springer Science+Business Media, LLC, part of Springer Nature 2020
Abstract A simple model of uniformly expanding, homogeneous Universe with a bulk viscosity is studied wherein the inflationary density decays due to viscous dissipation during the expansion phase of the Universe. The model is shown to generate the cosmic microwave background radiation. We also demonstrate that, at late times, the inflationary density asymptotically approaches a small finite constant value. Keywords Viscous universe · Cosmological constant · Bulk viscosity · Cosmic microwave background
Contents 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 Model set-up . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1 Approach 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2 Approach 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 General solution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1 Two examples for bulk viscosity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2 Energy conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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Sanved Kolekar [email protected] S. Shankaranarayanan [email protected] S. M. Chitre [email protected]
1
UM-DAE Centre for Excellence in Basic Sciences, Mumbai 400 098, India
2
Department of Physics, Indian Institute of Technology Bombay, Mumbai 400076, India 0123456789().: V,-vol
123
98
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1 Introduction The uniformity of large-scale structure of the Universe and the Gaussian nature of primordial fluctuations support the existence of an inflationary epoch in the early Universe [1,2]. In most inflation models, at the epoch of exit of inflation, the homogeneous inflaton begins to oscillate about the minimum of its potential. The inflaton decays into other forms of energy, such as that of matter and radiation, eventually giving the particle content of the Standard Model and perhaps even the dark matter. These more familiar forms of matter and radiation must eventually reach thermal equilibrium at temperatures higher than 1 MeV to recover the successful big-bang nucleosynthesis [1]. Even though inflation has been successful in explaining observations, the nature of the inflaton, however, remains unclear. The simplest inflationary models are driven by single scalar fields, while high-energy physics models usually involve many scalar fields (see, for instance, Refs. [3,
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