Thermodynamics of Irreversible Particle Creation Phenomena and Its Cosmological Consequence

  • Abhik Kumar Sanyal
  • Subhra Debnath


The study of particle creation phenomena at the expense of the gravitational field is of great research interest. It might solve the cosmological puzzle singlehandedly, without the need for either dark energy or modified theory of gravity. In the early universe, it serves the purpose of reheating which gave way to escape from inflationary phase to the hot Big Bang model. In the late universe, it instigates late-time cosmic acceleration, without affecting standard Big Bang Nucleosynthesis (BBN), Cosmic Microwave Background Radiation (CMBR), or Structure Formation. In this chapter, we briefly review the present status of cosmic evolution, develop the thermodynamics for irreversible particle creation phenomena, and study its consequences at the early as well as at the late universe.


Cosmology of particle creation Adiabatic irreversible thermodynamics 


  1. Abramo LRW, Finelli F (2003) Cosmological dynamics of the tachyon with an inverse power-law potential. Phys Lett B 575:165Google Scholar
  2. Achterberg A, Hurley K et al (2008) The Search for Muon Neutrinos from Northern Hemisphere Gamma-Ray Bursts with AMANDA, The IceCube collaboration, and The IPN collaboration. Astrophys J 674:357Google Scholar
  3. Aguirregabiria JM, Lazkoz R (2004) Tracking solutions in tachyon cosmology. Phys Rev D 69:123502Google Scholar
  4. Agullo I, Parker L (2011) Non-Gaussianities and the stimulated creation of quanta in the inflationary universe. Phys Rev D 83:063526Google Scholar
  5. Alam U, Sahni V (2002) Supernova constraints on braneworld dark energy. astro-ph/0209443Google Scholar
  6. Albrecht A, Steinhardt PJ (1982) Cosmology for grand unified theories with radiatively induced symmetry breaking. Phys Rev Lett 48:1220Google Scholar
  7. ANTARES Collaboration (2012) Measurement of atmospheric neutrino oscillations with the ANTARES neutrino telescope. Phys Lett B 714:224Google Scholar
  8. Armend´ariz-Pic´on C, Damour T, Mukhanov V (1999) k-Inflation. Phys Lett B 458:209Google Scholar
  9. Armend´ariz-Pic´on C, Mukhanov V, Steinhardt PJ (2000) Dynamical solution to the problem of a small cosmological constant and late-time cosmic acceleration. Phys Rev Lett 85:4438Google Scholar
  10. Armend´ariz-Pic´on C, Mukhanov V, Steinhardt PJ (2001) Essentials of k-essence. Phys Rev D 63:103510Google Scholar
  11. Bagla JS, Jassal HK, Padmanabhan T (2003) Cosmology with tachyon field as dark energy. Phys Rev D 67:063504Google Scholar
  12. Bahamonde S, Odintsov SD, Oikonomouand VK, Wright M (2016) Correspondence of F(R) gravity singularities in Jordan and Einstein frames. Annals Phys 373:96Google Scholar
  13. Banerjee N, Majumder B (2016) A question mark on the equivalence of Einstein and Jordan frames. Phys Lett B 754:129Google Scholar
  14. Banerjee A, Santos NO (1983) Anisotropic cosmological model with viscous fluid. J Math Phys 24(11):2689Google Scholar
  15. Banerjee A, Santos NO (1984) Spatially homogeneous cosmological models. Gen Rel Grav 16:217Google Scholar
  16. Banerjee A, Sanyal AK (1986) Homogeneous anisotropic cosmologiacl models with viscous fluid and magnetic field. Gen Rel Grav 18:1251Google Scholar
  17. Banerjee A, Sanyal AK (1988) Irrotational Bianchi Type-V Viscous Fluid Cosmology with Heat Flux. Gen Rel Grav 20:103Google Scholar
  18. Banerjee A, Duttachoudhury SB, Sanyal AK (1985) Bianchi Type I cosmological Model with a Viscous Fluid. J Math Phys 26:3010Google Scholar
  19. Banerjee A, Duttachoudhury SB, Sanyal AK (1986) Bianchi type-II cosmological model with viscous fluid. Gen Rel Grav 18:461Google Scholar
  20. Bardeen JM (1980) Gauge-invariant cosmological perturbations. Phys Rev D 22:1882Google Scholar
  21. Barrow JD (1990) Graduated inflationary universes. Phys Lett B 235:40Google Scholar
  22. Barrow JD (1995) Slow-roll inflation in scalar-tensor theories. Phys Rev D 51:2729Google Scholar
  23. Barrow JD, Saich P (1990) The behaviour of intermediate inflationary universes. Phys Lett B 249:406Google Scholar
  24. Bassett BA, Tsujikawa S, Wands D (2006) Inflation dynamics and reheating. Rev Mod Phys 78:537Google Scholar
  25. Belinskii VA, Khalatnikov IM (1975) Influence of viscosity on the character of cosmological evolution. Sov Phys JETP 42(2):205Google Scholar
  26. Bento MC, Bertolami O, Sen AA (2002) Generalized chaplygin gas, accelerated expansion and dark energy matter unification. Phys Rev D 66:043507Google Scholar
  27. Bergmann PG (1968) Comments on scalar tensor theory. Int J Theor Phys 1:25Google Scholar
  28. Bertotti B, Less L, Tortora P (2003) A test of general relativity with radio links with the Cassini spacecraft. Nature 425:374Google Scholar
  29. Bhadra A, Sarkar K, Datta DP, Nandi KK (2007) Brans–Dicke theory: Jordan versus Einstein frame. Mod Phys Lett A 22:367Google Scholar
  30. Bilic N, Tupper GB, Viollier RD (2002) Dark matter, dark energy and the chaplygin gas. astro-ph/0207423Google Scholar
  31. Birrell ND, Davies PCW (1982) Quantum fields in curved space. Cambridge University Press, CambridgeGoogle Scholar
  32. Brans C, Dicke RH (1961) Mach’s principle and a relativistic theory of gravitation. Phys Rev 124:925Google Scholar
  33. Brax P, Bruck C, Davis AC, Khoury J, Weltman A (2004) Detecting dark energy in orbit: the cosmological chameleon. Phys Rev D 70:123518Google Scholar
  34. Brax P, Bruck C, Mota DF, Nunes NJ, Winther HA (2010) Chameleons with field dependent couplings. Phys Rev D 82:083503Google Scholar
  35. Briscese F, Elizalde E, Nojiri S, Odintsov SD (2007) Phantom scalar dark energy as modified gravity: understanding the origin of the Big Rip singularity. Phys Lett B 646:105Google Scholar
  36. Brooker DJ, Odintsov SD, Woodard RP (2016) Precision predictions for the primordial power spectra from f (R) models of inflation. Nucl Phys B 911:318Google Scholar
  37. Cadarni N, Fabri R (1978) Production of entropy and viscous damping of anisotropy in homogeneous cosmological models - Bianchi type-I spaces. IL, Nuovo Cimento 44B:228Google Scholar
  38. Caldwell RR (2002) A phantom menace? Cosmological consequences of a dark energy component with super-negative equation of state. Phys Lett B 545:23Google Scholar
  39. Caldwell RR, Dave R, Steinhardt PJ (1998) Cosmological imprint of an energy component with general equation of state. Phys Rev Lett 80:1582Google Scholar
  40. Caldwell RR, Kamionkowski M, Weinberg NN (2003) Phantom energy and cosmic doomsday. Phys Rev Lett 91:071301Google Scholar
  41. Calvao MO, Lima JAS, Waga I (1992) On the thermodynamics of matter creation in cosmology. Phys Lett A 162:223Google Scholar
  42. Capozziello S, De Laurentis M (2011) Extended theories of gravity. Phys Rep 509:167Google Scholar
  43. Capozziello S, Nojiri S, Odintsov SD, Troisi A (2006) Cosmological viability of f(R)-gravity as an ideal fluid and its compatibility with a matter dominated phase. Phys Lett B 639:135Google Scholar
  44. Capozziello S, Martin-Moruno P, Rubano C (2010) Physical non-equivalence of the Jordan and Einstein frames. Phys Lett B 689:117Google Scholar
  45. Carroll SM, Sawicki I, Silvestri A, Trodden M (2006) Modified-source gravity and cosmological structure formation. New J Phys 8:323Google Scholar
  46. Chiba T, Okabe T, Yamaguchi M (2000) Kinetically driven quintessence. Phys Rev D 62:023511Google Scholar
  47. Choudhury TR, Padmanabhan T (2005) Cosmological parameters from supernova observations: a critical comparison of three data sets. Astron Astrophys 429:807Google Scholar
  48. Copeland EJ, Garousi MR, Sami M, Tsujikawa S (2005) What is needed of a tachyon if it is to be the dark energy? Phys Rev D 71:043003Google Scholar
  49. Debnath S, Sanyal AK (2011) Can particle creation phenomena replace dark energy? Class Quan Grav 28:145015Google Scholar
  50. Dick R (1998) Inequivalence of Jordan and Einstein frame: what is the low energy gravity In. string theory? Gen Rel Grav 30:435Google Scholar
  51. Dicke RH (1962a) Mach’s principle and invariance under transformation of units. Phys Rev 125:2163Google Scholar
  52. Dicke RH (1962b) Implications for cosmology of stellar and galactic evolution rates. Rev Mod Phys 34:110Google Scholar
  53. Dodelson S (2003) Modern Cosmology. Academic Press, San FranciscoGoogle Scholar
  54. Dvali G, Turner MS (2003) Dark Energy as a modification of the Friedmann equation. astro-ph/0301510Google Scholar
  55. Dvali G, Gabadadze G, Porrati M (2000) 4D gravity on a brane in 5D Minkowski space. Phys Lett B 485:208Google Scholar
  56. Elizalde E, Nojiri S, Odintsov SD (2004) Late-time cosmology in (phantom) scalar-tensor theory: dark energy and the cosmic speed-up. Phys Rev D 70:043539Google Scholar
  57. Ellis GFR (1971) Relativistic Cosmology, Rendicontidella Scuola Internazionale de Fisica “Enrico Fermi” XL VII, CorsoGoogle Scholar
  58. Faraoni V, Gunzig E (1999) Einstein frame or Jordan frame? Int J Theor Phys 38:217Google Scholar
  59. Faraoni V, Gunzig E, Nardone P (1999) Conformal transformations in classical gravitational theories and in cosmology. Fund Cosmic Phys 20:121Google Scholar
  60. Flanagan EE (2004) Palatini form of 1/R gravity. Phys Rev Lett 92:071101Google Scholar
  61. Freedman WL et al (2001) Final results from the hubble space telescope key project to measure the hubble constant. Astrophys J 553:47Google Scholar
  62. Friedmann A (1922) On the curvature of space. Z Phys 10:377Google Scholar
  63. Friedmann A (1924) On the possibility of a world with constant negative curvature of space. Z Phys 21:326Google Scholar
  64. Frieman J, Hill C, Stebbins A, Waga I (1995) Cosmology with ultra-light pseudo-nambu-goldstone bosons. Phys Rev Lett 75:2077Google Scholar
  65. Garriga J, Mukhanov V (1999) Perturbations in k-inflation. Phys Lett B 458:219Google Scholar
  66. Gasperini M, Veneziano G (1993) Inflation deflation and frame-independence in string cosmology. Mod Phys Lett A 8:3701Google Scholar
  67. Gasperini M, Veneziano G (1994) Dilaton production in string cosmology. Phys Rev D 50:2519Google Scholar
  68. Gibbons GW (2002) Cosmological evolution of the rolling tachyon. Phys Lett B 537:1Google Scholar
  69. Gubser SS, Khoury J (2004) Scalar self-interactions loosen constraints from fifth force searches. Phys Rev D 70:104001Google Scholar
  70. Gunzig E, Geheniau J, Prigogine I (1987) Entropy and Cosmology. Nature 330:621Google Scholar
  71. Guo ZK, Zhang YZ (2004) Cosmological scaling solutions of multiple tachyon fields with inverse square potentials. JCAP 0408:010Google Scholar
  72. Guth AH (1981) Inflationary universe: a possible solution to the horizon and flatness problems. Phys Rev D 23:347Google Scholar
  73. Haouat S, Chekireb R (2011) On the creation of scalar particles in a flat Robertson-Walker spacetime. Mod Phys Lett A 26:2639Google Scholar
  74. Haouat S, Chekireb R (2012) Effect of electromagnetic fields on the creation of scalar particles in a flat Robertson–Walker space-time. EPJC 72:2034Google Scholar
  75. Hawking SW (1974) Black hole explosions? Nature 248:30Google Scholar
  76. Hawking SW (1975) Particle creation by black holes. Comm Math Phys 43:199Google Scholar
  77. Hawking SW, Ellis GFR (1973) The large-scale structure of space-time. Cambridge University PressGoogle Scholar
  78. Heller M, Suszycki L (1974) Dust-filled viscous universes. Acta Phys Pol B 5:345Google Scholar
  79. Heller M, Limek ZK, Suszycki L (1973) Imperfect fluid Friedmannian cosmology. Astrophys Space Sci 20:205Google Scholar
  80. Hubble EP (1929) A relation between distance and radial velocity among extra-galactic nebulae. Proc Natl Acad Sci 15:168Google Scholar
  81. Islam JN (2002) An introduction to mathematical cosmology. Cambridge University PressGoogle Scholar
  82. Ito Y, Nojiri S (2009) Gauss-Bonnet chameleon mechanism of dark energy. Phys Rev D 79:103008Google Scholar
  83. Jackiw R (2000) A particle field theorist’s lectures on supersymmetric, non-abelian fluid mechanics and d-branes. arXiv: physics/0010042Google Scholar
  84. Kamenshchik AY, Moschella U, Pasquier V (2001) An alternative to quintessence. Phys Lett B 511:265Google Scholar
  85. Kearns E, Kajita T, Totsuka Y (1999) Detecting massive neutrinos. Scientific AmericanGoogle Scholar
  86. Khoury J, Weltman A (2004) Chameleon cosmology. Phys Rev D 69:044026Google Scholar
  87. Komatsu E et al (2011) Seven-year Wilkinson Microwave Anisotropy Probe (WMAP) observations: cosmological interpretation. Astrophys J Suppl Series 192:18Google Scholar
  88. La D, Steinhardt PJ (1989) Extended inflationary cosmology. Phys Rev Lett 62:376Google Scholar
  89. Landau LD, Lifshitz EM (1959) Fluid mechanics pergamon pressGoogle Scholar
  90. Lemaître G (1927) Ann Sci Soc Brussels (in French) 47A:41Google Scholar
  91. Lemaître G (1931) Translated in English. Monthly Not Royal Astrono Soc 91:483Google Scholar
  92. Lima JAS, Germano ASM, Abramo LRW (1996) FRW-type cosmologies with adiabatic matter creation. Phys Rev D 53:4287Google Scholar
  93. Lima JAS, Silva FE, Santos RC (2008) Accelerating cold dark matter cosmology (ΩΛ≡ 0). Class Quan Grav 25:205006Google Scholar
  94. Linde AD (1982) A new inflationary universe scenario a possible solution of the horizon, flatness homogeneity, isotropy and primordial monopole problems. Phys Lett B 108:389Google Scholar
  95. Linde AD (1983) Chaotic Inflation. Phys Lett B 129:177Google Scholar
  96. Magnano G, Sokolowski LM (1994) On physical equivalence between nonlinear gravity. Theories and a general relativistic self gravitating scalar field. Phys Rev D 50:50395059Google Scholar
  97. Mathiazhagan C, Johri VB (1984) An inflationary universe in Brans-Dicke theory: a hopeful sign of theoretical estimation of the gravitational constant. Class Quant Grav 1:L29Google Scholar
  98. Misner CW (1984) Neutrino viscosity and the isotropy of primordial blackbody radiation (1967) Phys Rev lett 19:533Google Scholar
  99. Mukhanov VF, Winitzki S (2007) Introduction to quantum fields in gravity. Cambridge: Cambridge University PressGoogle Scholar
  100. Mukhanov VF, Feldman HA, Brandenberger RH (1992) Theory of cosmological perturbations. Phys Rep 215:203Google Scholar
  101. Murphy GL (1973) Big-bang model without singularities. Phys Rev D 8(12):4231Google Scholar
  102. Narlikar JV (1983) Introduction to cosmology. Cambridge University PressGoogle Scholar
  103. NESTOR collaboration (1994) NESTOR: a neutrino particle astrophysics underwater laboratory for the Mediterranean Author links open overlay panel. Nucl Phys B 35:294Google Scholar
  104. Nightingale JD (1973) Independent investigations concerning bulk viscosity in relativistic homogeneous isotropic cosmologies. Astrphys J 185:105Google Scholar
  105. Nojiri S, Odintsov SD (2006) Modified f(R) gravity consistent with realistic cosmology: from matter dominated epoch to dark energy universe. Phys Rev D 74:086005Google Scholar
  106. Nojiri S, Odintsov SD (2011) Unified cosmic history in modified gravity: from F(R) theory to Lorentz non-invariant models. Phys Rep 505:59Google Scholar
  107. Nosengo N (2012) Gran Sasso: Chamber of physics. Nature 485:435Google Scholar
  108. Padmanabhan T (2002) Accelerated expansion of the universe driven by tachyonic matter. Phys Rev D 66:021301Google Scholar
  109. Papastamatiou J, Parker L (1979) Asymmetric creation of matter and antimatter in the expanding universe. Phys Rev D 19:2283Google Scholar
  110. Parker L (1968) Particle creation in expanding universes. Phys Rev Lett 21:562Google Scholar
  111. Parker L (1969) Quantized fields and particle creation in expanding universes. I. Phys Rev 183:1057Google Scholar
  112. Parker L (1971) Quantized fields and particle creation in expanding universes. II. Phys Rev D 3:346Google Scholar
  113. Peebles PJE (1980) The large scale structure of the universe. Princeton University PressGoogle Scholar
  114. Peebles PJE (1993) Principles of physical cosmology. Princeton University PressGoogle Scholar
  115. Peebles PJE, Ratra B (1988) Cosmology with a time-variable cosmological ‘constant’. Ap J Lett 325:L17Google Scholar
  116. Penzias AA, Wilson RW (1965) A measurement of excess antenna temperature at 4080 Mc/s. Astrophys J 142:419Google Scholar
  117. Perlmutter S et al (1999) Measurements of omega and lambda from 42 high-redshift supernovae. Astrophys J 517:565Google Scholar
  118. Planck collaboration (2014) Planck 2013 results-I. Overview of products and scientific results.Astron Astrophys 571:A1Google Scholar
  119. Planck collaboration P. A. R. Ade (2016) Planck 2015 results-XIII. Cosmological parameters. Astron Astrophys 594:A20Google Scholar
  120. Prigogine I (1989) Thermodynamics and cosmology. Int J Theor Phys 28:927Google Scholar
  121. Prigogine I, Geheniau J, Gunzig E, Nardone P (1989) Thermodynamics and cosmology. Gen Rel Grav 21:767Google Scholar
  122. Ratra B, Peebles PJE (1988) Cosmological consequences of a rolling homogeneous scalar field. Phys Rev D 37:3406Google Scholar
  123. Reiss AG et al (2011) A 3% Solution: determination of the hubble constant with the hubble space telescope and wide field camera 3. Astrophys J 730:119Google Scholar
  124. Ribeiro MB, Sanyal AK (1987) Bianchi VI0 viscous fluid cosmology with magnetic field. J Math Phys 28:657Google Scholar
  125. Riess AG et al (1998) Observational evidence from supernovae for an accelerating universe and a cosmological constant. Astron J 116:1009Google Scholar
  126. Sachs RK, Wolfe AM (1967) Perturbations of a cosmological model and angular variations of the microwave background. Astrophys J 147:73Google Scholar
  127. Sahni V, Shtanov Y (2003) Braneworld models of dark energy. JCAP 0311:014Google Scholar
  128. Sanyal AK (2007) If Gauss-Bonnet interaction plays the role of dark energy. Phys Lett B 645:1Google Scholar
  129. Sanyal AK (2008) Intermediate inflation or late time acceleration? Adv High Energy Phys 2008:630414Google Scholar
  130. Sanyal AK (2009a) Smooth crossing of ωΛ = −1 line in a single scalar field model. Adv High Energy Phys 2009:612063Google Scholar
  131. Sanyal AK (2009b) Transient crossing of phantom divide line ωΛ = −1 under Gauss-Bonnet interaction. Gen Rel Grav 41:1511Google Scholar
  132. Sen A (2002a) Rolling Tachyon. JHEP 0204:048Google Scholar
  133. Sen A (2002b) Tachyon Matter. JHEP 0207:065Google Scholar
  134. Sk N, Sanyal AK (2017) Why scalar-tensor equivalent theories are not physically equivalent? IJMPD 26:1750162Google Scholar
  135. Soussa ME, Woodard RP (2004) The force of gravity from a lagrangian containing inverse powers of the ricci scalar. Gen Rel Grav 36:855Google Scholar
  136. Spergel DN et al (2007) Wilkinson Microwave Anisotropy Probe (WMAP) Three year results: implications for cosmology. Astrophys J suppl 170:377Google Scholar
  137. Spindel P (1981) Mass formula in a cosmogenesis model. Phys Lett 107:361Google Scholar
  138. Starobinsky AA (1980) A new type of isotropic cosmological models without singularity. Phys Lett B 91:99Google Scholar
  139. Steigman G, Santos RC, Lima JAS (2009) An accelerating cosmology without dark energy. J Cosmol Astropart Phys JCAP06:33Google Scholar
  140. Steinhardt PJ, Accetta FS (1990) Hyperextended inflation. Phys Rev Lett 64:2740Google Scholar
  141. Treciokas R, Ellis GFR (1971) Isotropic solutions of the Einstein-Boltzmann equations. Comm Math Phys 23:1Google Scholar
  142. Tsujikawa S, Tamaki T, Tavakol R (2009) Chameleon scalar fields in relativistic gravitational backgrounds. JCAP 0905:020Google Scholar
  143. Vollick DN (2003) 1/R curvature corrections as the source of the cosmological acceleration. Phys Rev D 68:063510Google Scholar
  144. Vollick DN (2004) On the viability of the Palatini form of 1/R gravity. Class Quant Grav 21:3813Google Scholar
  145. Wagner RV (1970) Scalar-tensor theory and gravitational waves. Phys Rev D 1:3209Google Scholar
  146. Weinberg S (1971) Entropy generation and the survival of protogalaxies in an expanding universe. Astrophys J 168:175Google Scholar
  147. Weinberg S (1972) Gravitation and cosmology. Wiley, New YorkGoogle Scholar
  148. Zimdahl W, Pavón D (1993) Cosmology with adiabatic matter creation. Phys Lett A 176:57Google Scholar
  149. Zimdahl W, Triginer J, Pavón D (1996) Collisional equilibrium, particle production, and the inflationary universe. Phys Rev D 54:6101Google Scholar
  150. Zlatev I, Wang LM, Steinhardt PJ (1999) Quintessence, cosmic coincidence, and the cosmological constant. Phys Rev Lett 82:896Google Scholar

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Authors and Affiliations

  1. 1.Department of Physics, Jangipur CollegeUniversity of KalyaniJangipur, MurshidabadIndia

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