Energy-momentum tensor of a massless scalar quantum field in a Robertson-Walker universe

Gravitational anomalies on the Newton-Cartan background

“…In considering relativistic systems with a symmetric stress-energy tensor, the trace anomaly arises when the quantum stress-energy tensor is not traceless, while its failure to be conserved results in the diffeomorphism anomaly. These anomalies have important consequences in black holes physics and cosmology [4][5][6][7][8][9][10][11][12][13][14][15][16][17], as well as in the computation of transport coefficients and response functions of condensed matter systems [18][19][20][21][22][23][24][25][26][27][28]. Gravitational anomalies are in addition background dependent, as evident from the difference of Lifshitz anomalies from those of relativistic backgrounds.…”

Casimir effect, Achucarro-Ortiz black hole, and the cosmological constant

“…It describes the physical character of the quantum field at a spacetime point x and it is also the source of gravity in this gravitational background. There is a plethora of field theoretical procedures [1,2,3,4,5], known as regularization techniques, for computing a finite and renormalized < T µν > reg such as the dimensional regularization [6,7,8], Green's function method [9,10], heat kernel method [11,12], zeta function regularization [13], point-splitting method [14,15,16], Pauli-Villars regularization [17]. In this article, we are going to derive the exact form of the stress tensor of a massless scalar field by implementing some general properties of the renormalized stress tensor known as Wald's axioms [19,20] avoiding in this way to employ any of the above-mentioned techniques.…”

Starobinsky-type inflation in dynamical supergravity breaking scenarios

“…In particular, we shall demonstrate the compatibility of this scenario with Starobinsky-like [2] inflationary scenarios, which in our case can characterise the massive gravitino phase. As we shall argue, this is a second inflationary phase, that may succeed a first inflation which occurs in the flat region of the one-loop effective potential for the gravitino condensate field [3].Starobinsky inflation is a model for obtaining a de Sitter (inflationary) cosmological solution to gravitational equations arising from a (four space-time-dimensional) action that includes higher curvature terms, specifically of the type in which the quadratic curvature corrections consist only of scalar curvature terms [2]where κ 2 = 8πG, and G = 1/m 2 P is Newton's (gravitational) constant in four space-time dimensions, with m P the Planck mass, and M is a constant of mass dimension one, characteristic of the model.The important feature of this model is that inflationary dynamics are driven by the purely gravitational sector, through the R 2 terms, and the scale of inflation is linked to M. From a microscopic point of view, the scalar curvature-squared terms in (1) are viewed as the result of quantum fluctuations (at one-loop level) of conformal (massless or high energy) matter fields of various spins, which have been integrated out in the relevant path integral in a curved background space-time [4]. The quantum mechanics of this model, by means of tunneling of the Universe from a state of "nothing" to the inflationary phase of ref.…”