Effects of quantum gravity on the inflationary parameters and thermodynamics of the early universe
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Effects of quantum gravity on the inflationary parameters and thermodynamics of the early universe A. Tawfik · H. Magdy · Ahmed Farag Ali
Received: 17 September 2012 / Accepted: 14 March 2013 / Published online: 2 April 2013 © Springer Science+Business Media New York 2013
Abstract The effects of generalized uncertainty principle (GUP) on the inflationary dynamics and the thermodynamics of the early universe are studied. Using the GUP approach, the tensorial and scalar density fluctuations in the inflation era are evaluated and compared with the standard case. We find a good agreement with the Wilkinson Microwave Anisotropy Probe data. Assuming that a quantum gas of scalar particles is confined within a thin layer near the apparent horizon of the Friedmann-LemaitreRobertson-Walker universe which satisfies the boundary condition, the number and entropy densities and the free energy arising form the quantum states are calculated using the GUP approach. A qualitative estimation for effects of the quantum gravity on all these thermodynamic quantities is introduced. Keywords
Inflation · Quantum gravity phenomenology
A. Tawfik (B) · H. Magdy Egyptian Center for Theoretical Physics (ECTP), MTI University, Cairo, Egypt e-mail: [email protected] H. Magdy e-mail: [email protected] A. Tawfik Research Center for Einstein Physics, Freie-University Berlin, Berlin, Germany e-mail: [email protected] A. Farag Ali Physics Department, Faculty of Science, Benha University, Benha 13518, Egypt e-mail: [email protected]; [email protected]
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1 Introduction The idea that the uncertainty principle would be affected by the quantum gravity has been suggested couple decades ago [1]. Should the theories of quantum gravity, such as string theory, doubly special relativity and black hole physics be confirmed, our understanding of the basic laws and principles of physics turn to be considerably different, especially at very high energies or short distances [2–11]. Various examples can be mentioned to support this phenomena. In the context of polymer quantization, the commutation relations are given in terms of the polymer mass scale [12]. Also, the standard commutation relations in the quantum mechanics are conjectured to be changed or better to say generalized at the length scales of the order of Planck’s length [8,9,13–15]. Such modifications are supposed to play an essential role in the quantum gravitational corrections at very high energy [16]. Accordingly, the standard uncertainty relation of quantum mechanics is replaced by a gravitational uncertainty relation having a minimal observable length of the order of Planck’s length [10,11,17–20]. The existence of a minimal length is one of the most interesting predictions of such new physics. These can be seen as the consequences of the string theory, since strings can not interact at distances smaller than their size which leads to a generalized uncertainty principle (GUP) [2]. Furthermore, the black hole physics suggests that the uncertainty relation
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