Stress-energy tensor of the quantized massive fields in Friedman-Robertson-Walker spacetimes

Abstract

The approximate stress-energy tensor of the quantized massive scalar, spinor and vector fields in the spatially flat Friedman-Robertson-Walker universe is constructed. It is shown that for the scalar fields with arbitrary curvature coupling, ξ, the stress-energy tensor calculated within the framework of the Schwinger-DeWitt approach is identical to the analogous tensor constructed in the adiabatic vacuum. Similarly, the Schwinger-DeWitt stress-energy tensor for the fields of spin 1/2 and 1 coincides with the analogous result calculated by the Zeldovich-Starobinsky method. The stress-energy tensor thus obtained are subsequently used in the back reaction problem. It is shown that for pure semiclassical Einstein field equations with the vanishing cosmological constant and the source term consisting exclusively of its quantum part there are no self-consistent exponential solutions driven by the spinor and vector fields. A similar situation takes place for the scalar field if the coupling constant belongs to the interval ξ > ∼ 0.1. For a positive cosmological constant the expansion slows down for all considered types of massive fields except for minimally coupled scalar field. The perturbative approach to the problem is briefly discussed and possible generalizations of the stress-energy tensor are indicated.

Stability of the effective potential of the gauge-less top-Higgs model in curved spacetime

“…Details of these methods were described in many textbooks, e.g., see [13,16]. On the application side, this approach was used to construct the renormalized stress-energy tensor for non-interacting scalar, spinor and vector fields in various black hole spacetimes [17][18][19][20][21] and in cosmological one [22]. Recently, it was applied to the investigations of the inflaton-curvaton dynamics [23] and the stability of the Higgs potential [24] during the inflationary era as well as to the problem of the present-day acceleration of the Universe expansion [25,26].…”

Renormalized stress tensor for massive fields in Kerr-Newman spacetime

“…[23][24][25][26][27][28][29][30][31][32][33][34][35][36][37] for applications to black holes, wormholes and black strings and Refs. [38,39] for a recent work concerning the Friedmann-Lemaître-Robertson-Walker universes) and it is important to note that the approximate RSETs obtained from the DeWitt-Schwinger expansion of the effective action seem to be in good agreement with exact results (see Ref. [26] where this has been discussed for the Reissner-Nordström black hole).…”

Stress-energy Tensor of the Quantized Massive Fields in Spatially-flat $D$-dimensional Friedmann--Robertson--Walker Spacetimes

“…On the other hand, the semiclassical analysis can teach us a lot about the influence of the quantized fields on the black hole interior and about the tendency of the changes of the background geometry as the singularity is approached. Of course, from the point of view of the present work, the most important are the results obtained in cosmology (see e.g., Refs [13][14][15][16][17][18][19][20][21][22][23][24][25][26][27] and the references cited therein) and in the black hole interiors [28][29][30][31][32][33].…”