Abstract
The time-dependent cosmological term arises from the energy-momentum tensor calculated in a state different from the ground state. We discuss the expectation value of the energy-momentum tensor on the right hand side of Einstein equations in various (approximate) quantum pure as well as mixed states. We apply the classical slow-roll field evolution as well as the Starobinsky and warm inflation stochastic equations in order to calculate the expectation value. We show that, in the state concentrated at the local maximum of the double-well potential, the expectation value is decreasing exponentially. We confirm the descent of the expectation value in the stochastic inflation model. We calculate the cosmological constant Λ at large time as the expectation value of the energy density with respect to the stationary probability distribution. We show that Λ ≃ γ 4 3 where γ is the thermal dissipation rate.
Highlights
In the description of inflation, it is understood that at the early stages of the universe evolution quantum physics is relevant
The diffusion constant γ2 is proportional to the temperature at the end of the radiation era in warm inflation models
The cosmological term can be interpreted as the expectation value of the energy density in a quantum state describing the universe evolution
Summary
In the description of inflation, it is understood that at the early stages of the universe evolution quantum physics is relevant. We consider a method of the description of the vacuum decay based on the slow-roll and diffusion approximations to the quantum evolution in an expanding universe [18,19] This is a long wave approximation which neglects the second-order derivatives in equations of motion and first-order derivatives in the energy-momentum tensor. According to the authors of [18,19,22,23], in a slow roll approximation, the field evolution in such a quantum state can be obtained as a solution of a stochastic equation with quantum and thermal noise. We show that the cosmological constant at large time is proportional to the thermal diffusion constant
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