Quantum effects on conformally coupled scalars during inflation

The effects arising from the small (quantum) scale in the early universe help us to understand large (cosmological) scale structure formation in today's universe. Throughout this thesis, we are interested in these small scale effects in the early universe. First of all, we search to find the answer to the fundamental question "What is the source of these quantum effects?" in this thesis. The answer to this question is given by the particular example, the interactions between the "massless conformally coupled scalars (φ ̃)" and "gravitons (hμν)" in the early universe which lead to quantum effects. The reason for the particularly choice of these two particles can be summarized as: The quantum effects stem from the particles created in vacuum. In flat space, virtual particles affect on these particles created in vacuum. These effects of virtual particles diminish and finally disappear at the Planck time. But the expansion of curved space-time alters 'Heisenberg's energy-time uncertainty principle' (∆E ∆t > h ̄/2), allowing virtual particles to survive longer than in flat space. The reaction rate of interacted virtual particles increase in the expanding space-time if these particles are massless and conformally non invariant. In inflation scenarios, the expansion of curved space-time can lead to particle creation by increasing the existence time of virtual particle pairs in vacuum. If the expansion is accelerated, the effect is strongest and the virtual particles are massless and do not possess conformal symmetry. Therefore, the well known examples of the kind of these particles are massless, minimally coupled (MMC) scalars and gravitons in the literature. They can mediate large quantum effects during inflation. Also, the named as cosmological perturbations as firstly quantum gravitational observables that were predicted by Mukhanov and Chibisov at 1981 for the scalar part and by Starobinsky at 1979 for the tensor part. The MMC scalars and gravitons are the source of scalar (WMAP9, Planck) and tensor perturbations (B-mode polarization), respectively, predicted by inflationary theories. The observables from these cosmological perturbation came into prominence via Cosmic Microwave Background (CMB) power spectrum. In this thesis, the interaction between particularly "massless conformally coupled scalars" and "graviton" is taken as the source of the quantum effects during inflation and these effects are calculated as the corrections coming from the first order level. In order to analyze these effects, the effective field equation are solved. In Chapters 2. and 3., the calculations of leading order quantum gravity corrections from these interactions are detaily given in de Sitter inflation time. Firstly, the corresponding only the lowest order Feynman diagrams, i.e., one-loop order Feynman diagrams, are calculated applying the perturbation method in terms of the loop-counting parameter (κ2 ≡ 16πG). Second, fully renormalized self-mass-squared (SMS) (iM2(x;x′)) for conformally coupled scalars (CCS) is obtained by using special calculation technique, dimensional regularization. In this technique, the counterterms help to extract the finite terms from the divergences. The fully renormalized self-mass-squared is obtained for every interaction (conformal-conformal interaction, kinetic-kinetic interaction, cross interaction), separately. Then, the total of them is given as −iM2(x;x′) = −iM2(x;x′) + −iM2(x;x′) + −iM2 (x;x′), C K cross here C and K denote conformal and kinetic interactions, respectively. The total of them −iM2(x;x′) is needed for the next step of the calculations, as μν ̃ 1 ̃ ̃ 4′2 ′ ̃′ ∂μ −g ̃g ̃ ∂ν φ(x)−6φ(x)R − d xM (x;x)φ(x) =0. These difficult calculations and their outcomes are published as two works. In Chapter 4., the Schwinger-Keldysh linearized effective field equation 2 ̃⃗ 0′ 3′2′ ̃′⃗ ∂ Φ1(x;k)− dη d xM1(x;x)Φ0(x;k) =0. ηi is solved by applying the perturbation method in terms of loop-counting parameter to the obtained self-mass-squared outcomes and conformally coupling scalar as ∞ M2(x;x′) = ∑κ2lMl2(x;x′), l=1 ∞∞⃗ Φ ̃(x;⃗k) = ∑κ2lΦ ̃l(x;⃗k)= ∑κ2lu ̃l(η,k)×eik·⃗x , l=0 l=0 and using some special integral techniques. It is seen that the found quantum corrected scalar mode functions (u ̃l(η,k)) have a secular growth effect behaviour, proportional to a logarithm of the scale factor at late times with physical time. The all calculations' details and their outcomes are published in the third work. In Chapter 5., the effect of loop corrections to primordial non-Gaussianity of Cosmic Microwave Background is investigated and the findings from it can be sorted as: A huge value for the non-Gaussianity which would exceed the observed value by at least 30 orders of magnitude may be obtained for single scalar inflaton. It is shown that the non-Gaussianity is a better place for quantum gravitational corrections: While power spectrum is related to the magnitude of mode function, non-Gaussianity is related to the time derivative of the mode function. All details are included in the published last work. All outcomes are summed and the recommended future works are presented in Chapter 6.. In this way, the expected outcomes coming from quantum gravity effects for particular example from the interaction between a "massless conformally coupled scalars" and a "graviton" during inflation time are investigated in this thesis.