Energy-momentum tensor of field fluctuations in massive chaotic inflation

Physical Review D - Particles, Fields, Gravitation and Cosmology

Volumn 65, Issue 10, 2002, Pages 14-

  Finelli, F ^a   Marozzi, G ^a   Vacca, G P ^a   Venturi, G ^a  

^a PURDUE UNIVERSITY   (United States)

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EID: 85038291338     PISSN: 15507998     EISSN: 15502368     Source Type: Journal    
DOI: 10.1103/PhysRevD.65.103521     Document Type: Article

References (44)

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34. Let us remember that the evaluation of the renormalized expectation value of (Formula presented) is limited by the approximation of neglecting the infrared part of the integral in the expectation values. This infrared part leads to a contribution (Formula presented) in the fourth order adiabatic quantities, such as in Eq. (B8). For the adiabatic counterterms this approximation is thus very good. Instead, for the bare renormalized expectation value of (Formula presented), we (numerically) estimate this infrared contribution to be (Formula presented). Such a term is negligible with respect to the leading terms (Formula presented) in the final finite renormalized value of (Formula presented) (45), but is of the same order of magnitude of the nonleading terms present in Eq. (45).
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40. We note that Eq. (49) should also be correct for large (Formula presented). In this case (Formula presented) is imaginary, but the solutions with the Bessel functions are valid, and so is the dimensional regularization. From Eq. (49) it is evident that the leading behavior of the EMT would be (Formula presented), which would correspond to a large renormalized vacuum energy. This result appears puzzling if one believes that there should not be significant particle production for (Formula presented). However, this behavior can be understood in the framework of adiabatic subtraction. Even for a large mass m the Green’s function of a test field in de Sitter space has a power-law decay, while in Minkowski space-time a massive scalar field has an exponential decay. Since the part one subtracts in the adiabatic subtraction is basically constructed perturbatively from the solutions for Minkowski space-time, we think that the subtraction is not sufficient to eliminate this large vacuum energy contribution.
41. The renormalization of the EMT of inflaton fluctuations calculated without the cutoff introduced in Eq. (31) would lead to a result which coincides with the Bunch-Davies one (49) for (Formula presented). However, this result would be singular since (Formula presented), and the singularity due to (Formula presented) in the EMT persists since (Formula presented). As happens in the de Sitter case in the massless limit for minimally coupled scalar fields, the Bunch-Davies vacuum leads to singular expectations values. In the de Sitter case the two point function is singular, and for massive chaotic inflation both the two point function and (Formula presented) are singular. In the de Sitter case, on switching to the Allen-Folacci vacuum 14, one can have a regular two-point function, which however loses some de Sitter symmetries (it grows in time). It is interesting that we obtain a result which reduces to the Allen-Folacci one when (Formula presented), on just requiring regular expectation values. This means that our procedure with the cutoff is consistent with the redefinition of the zero mode for massless minimally coupled scalar fields, which leads to the Allen-Folacci vacuum.
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