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Tommi Markkanen

Publications and source records attributed to Tommi Markkanen.

36 records · Page 2Linked to original sources
arXiv2018

Renormalization of the inflationary perturbations revisited

In this work we clarify aspects of renormalization on curved backgrounds focussing on the potential ramifications on the amplitude of inflationary perturbations. We provide an alternate view of the often used adiabatic prescription by deriving a correspondence between the adiabatic subtraction terms and traditional renormalization. Specifically, we show how adiabatic subtraction can be expressed as a set of counter terms that are introduced by redefining the bare parameters of the action. Our representation of adiabatic subtraction then allows us to easily find other renormalization prescriptions differing only in the finite parts of the counter terms. As our main result, we present for quadratic inflation how one may consistently express the renormalization of the spectrum of perturbations from inflation as a redefinition of the bare cosmological constant and Planck mass such that the observable predictions coincide with the unrenormalized result.

hep-th↗
arXiv2018

Quantum corrections to quartic inflation with a non-minimal coupling: metric vs. Palatini

We study models of quartic inflation where the inflaton field $ϕ$ is coupled non-minimally to gravity, $ξϕ^2 R$, and perform a study of quantum corrections in curved space-time at one-loop level. We specifically focus on comparing results between the metric and Palatini theories of gravity. Transformation from the Jordan to the Einstein frame gives different results for the two formulations and by using an effective field theory expansion we derive the appropriate $β$-functions and the renormalisation group improved effective potentials in curved space for both cases in the Einstein frame. In particular, we show that in both formalisms the Einstein frame depends on the order of perturbation theory but that the flatness of the potential is unaltered by quantum corrections.

gr-qc↗
arXiv2018

Light scalars on cosmological backgrounds

We study the behaviour of a light quartically self-interacting scalar field $ϕ$ on curved backgrounds that may be described with the cosmological equation state parameter $w$. At leading order in the non-perturbative 2PI expansion we find a general formula for the variance $\langle\hatϕ^2\rangle$ and show for several previously unexplored cases, including matter domination and kination, that the curvature of space can induce a significant excitation of the field. We discuss how the generation of a non-zero variance for $w\neq-1$ can be understood as a process of self-regulation of the infrared divergences very similarly to what is known to occur in de Sitter space. To conclude, the appearance of an effective mass due to self-interaction is generic for a light scalar in curved space and can have important implications for reheating, vacuum stability and dark matter generation.

gr-qc↗
arXiv2017

Do metric fluctuations affect the Higgs dynamics during inflation?

We show that the dynamics of the Higgs field during inflation is not affected by metric fluctuations if the Higgs is an energetically subdominant light spectator. For Standard Model parameters we find that couplings between Higgs and metric fluctuations are suppressed by $\mathcal{O}(10^{-7})$. They are negligible compared to both pure Higgs terms in the effective potential and the unavoidable non-minimal Higgs coupling to background scalar curvature. The question of the electroweak vacuum instability during high energy scale inflation can therefore be studied consistently using the Jordan frame action in a Friedmann--Lemaître--Robertson--Walker metric, where the Higgs-curvature coupling enters as an effective mass contribution. Similar results apply for other light spectator scalar fields during inflation.

hep-ph↗
arXiv2017

Decoherence Can Relax Cosmic Acceleration

In this work we investigate the semi-classical backreaction for a quantised conformal scalar field and classical vacuum energy. In contrast to the usual approximation of a closed system, our analysis includes an environmental sector such that a quantum-to-classical transition can take place. We show that when the system decoheres into a mixed state with particle number as the classical observable de Sitter space is destabilized, which is observable as a gradually decreasing Hubble rate. In particular we show that at late times this mechanism can drive the curvature of the Universe to zero and has an interpretation as the decay of the vacuum energy demonstrating that quantum effects can be relevant for the fate of the Universe.

hep-th↗
arXiv2017

Decoherence Can Relax Cosmic Acceleration: an Example

We investigate back reaction in de Sitter space in an approach where only states that are observationally accessible are included in the density matrix. Using the Bunch-Davies vacuum as the initial condition we find for a conformal scalar field and a cosmological constant that tracing over the unobservable states beyond the cosmological horizon leads to a thermal spectrum of particles and that such a configuration is unstable under semi-classical back reaction. It is concluded that this prescription results in an instability of de Sitter space with a gradually increasing horizon size.

gr-qc↗
arXiv2017

Vacuum Stability in the Early Universe and the Backreaction of Classical Gravity

In the case of a metastable electroweak vacuum the quantum corrected effective potential plays a crucial role in the potential instability of the Standard Model. In the Early Universe, in particular during inflation and reheating, this instability can be triggered leading to catastrophic vacuum decay. We discuss how the large spacetime curvature of the Early Universe can be incorporated in the calculation and in many cases significantly modify the flat space prediction. The two key new elements are the unavoidable generation of the non-minimal coupling between the Higgs field and the scalar curvature of gravity and a curvature induced contribution to the running of the constants. For the minimal set up of the Standard Model and a decoupled inflation sector we show how a metastable vacuum can lead to very tight bounds for the non-minimal coupling. We also discuss a novel and very much related dark matter generation mechanism.

hep-ph↗
arXiv2017

Narrowing the window of inflationary magnetogenesis

We consider inflationary magnetogenesis where the conformal symmetry is broken by the term $f^2(ϕ) F_{αβ} F^{αβ}$. We assume that the magnetic field power spectrum today between 0.1 and $10^4$ Mpc is a power law, with upper and lower limits from observation. This fixes $f$ to be close to a power law in conformal time in the window during inflation when the modes observed today are generated. In contrast to previous work, we do not make any assumptions about the form of $f$ outside these scales. We cover all possible reheating histories, described by an average equation of state $-1/3 <\bar{w} <1$. Requiring that strong coupling and large backreaction are avoided both at the background and perturbative level, we find the bound $δ_{B_0} < 5 \times10^{-15} \left( \frac{r}{0.07} \right)^{1/2} κ\mathrm{G}$ for the magnetic field generated by inflation, where $r$ is the tensor-to-scalar ratio and $κ$ is a constant related to the form of $f$. This estimate has an uncertainty of one order of magnitude related to our approximations. The parameter $κ$ is $<100$, and values $\gtrsim1$ require a highly fine-tuned form of $f$; typical values are orders of magnitude smaller.

astro-ph.CO↗
arXiv2017

Dark matter from gravitational particle production at reheating

We show that curvature induced particle production at reheating generates adiabatic dark matter if there are non-minimally coupled spectator scalars weakly coupled to visible matter. The observed dark matter abundance implies an upper bound on spectator masses $m$ and non-minimal coupling values $ξ$. For example, assuming quadratic inflation, instant reheating and a single spectator scalar with only gravitational couplings, the observed dark matter abundance is obtained for $m\sim 0.1$ GeV and $ξ\sim 1$. Larger mass and coupling values of the spectator are excluded as they would lead to overproduction of dark matter.

astro-ph.CO↗
arXiv2017

Massive scalar field evolution in de Sitter

The behaviour of a massive, non-interacting and non-minimally coupled quantised scalar field in an expanding de Sitter background is investigated by solving the field evolution for an arbitrary initial state. In this approach there is no need to choose a vacuum in order to provide a definition for particle states. We conclude that the expanding de Sitter space is a stable equilibrium configuration under small perturbations of the initial conditions. Depending on the initial state, the energy density can approach its asymptotic value from above or below, the latter of which implies a violation of the weak energy condition. The backreaction of the quantum corrections can therefore lead to a phase of super-acceleration also in the non-interacting massive case.

gr-qc↗
arXiv2015

Spacetime curvature and Higgs stability after inflation

We investigate the dynamics of the Higgs field at the end of inflation in the minimal scenario consisting of an inflaton field coupled to the Standard Model only through the non-minimal gravitational coupling $ξ$ of the Higgs field. Such a coupling is required by renormalisation of the Standard Model in curved space, and in the current scenario also by vacuum stability during high-scale inflation. We find that for $ξ\gtrsim 1$, rapidly changing spacetime curvature at the end of inflation leads to significant production of Higgs particles, potentially triggering a transition to a negative-energy Planck scale vacuum state and causing an immediate collapse of the Universe.

hep-ph↗
arXiv2015

Curvature induced running of the cosmological constant

In this work we investigate the renormalization group flow of the cosmological constant $Λ$ induced by the change in space-time curvature in the electroweak vacuum. We calculate the generic magnitude resulting from running in the standard model in a subtraction scheme that respects the Appelquist-Carazzone decoupling theorem. Interestingly, we find in this prescription that for a non-minimal coupling $ξ\lesssim 10^4$ the magnitude of the generated contribution remains below the value consistent with observations.

gr-qc↗
arXiv2015

Inflation without quantum gravity

It is sometimes argued that observation of tensor modes from inflation would provide the first evidence for quantum gravity. However, in the usual inflationary formalism, also the scalar modes involve quantised metric perturbations. We consider the issue in a semiclassical setup in which only matter is quantised, and spacetime is classical. We assume that the state collapses on a spacelike hypersurface, and find that the spectrum of scalar perturbations depends on the hypersurface. For reasonable choices, we can recover the usual inflationary predictions for scalar perturbations in minimally coupled single-field models. In models where non-minimal coupling to gravity is important and the field value is sub-Planckian, we do not get a nearly scale-invariant spectrum of scalar perturbations. As gravitational waves are only produced at second order, the tensor-to-scalar ratio is negligible. We conclude that detection of inflationary gravitational waves would indeed be needed to have observational evidence of quantisation of gravity.

astro-ph.CO↗
arXiv2014

Spacetime curvature and the Higgs stability during inflation

It has been claimed that the electroweak vacuum may be unstable during inflation due to large fluctuations of order $H$ in case of a high inflationary scale as suggested by BICEP2. We compute the Standard Model Higgs effective potential including UV-induced curvature corrections at one-loop level. We find that for a high inflationary scale a large curvature mass is generated due to RG running of non-minimal coupling $ξ$, which either stabilizes the potential against fluctuations for $ξ_{\rm EW} \gtrsim 6\cdot 10^{-2}$, or destabilizes it for $ξ_{\rm EW} \lesssim 2 \cdot 10^{-2}$ when the generated curvature mass is negative. Only in the narrow intermediate region the effect of the curvature mass may be significantly smaller.

hep-ph↗
arXiv2014

Quantum corrections to scalar field dynamics in a slow-roll space-time

We consider the dynamics of a quantum scalar field in the background of a slow-roll inflating Universe. We compute the one-loop quantum corrections to the field and Friedmann equation of motion, in both a 1PI and a 2PI expansion, to leading order in slow-roll. Generalizing the works of [1-3], we then solve these equations to compute the effect on the primordial power spectrum, for the case of a self-interacting inflaton and a self-interacting spectator field. We find that for the inflaton the corrections are negligible due to the smallness of the coupling constant despite the large IR enhancement of the loop contributions. For a curvaton scenario, on the other hand, we find tension in using the 1PI loop corrections, which may indicate that the quantum corrections could be non-perturbatively large in this case, thus requiring resummation.

hep-ph↗
arXiv2013

A Simple Method for One-Loop Renormalization in Curved Space-Time

We present a simple method for deriving the renormalization counterterms from the components of the energy-momentum tensor in curved space-time. This method allows full control over the finite parts of the counterterms and provides explicit expressions for each term separately. As an example, the method is used for the self-interacting scalar field in a Friedmann-Robertson-Walker metric in the adiabatic approximation, where we calculate the renormalized equation of motion for the field and the renormalized components of the energy-momentum tensor to fourth adiabatic order while including interactions to one-loop order. Within this formalism the trace anomaly, including contributions from interactions, is shown to have a simple derivation. We compare our results to those obtained by two standard methods, finding agreement with the Schwinger-DeWitt expansion but disagreement with adiabatic subtractions for interacting theories.

hep-th↗
arXiv2012

Quantum Corrections to Inflaton and Curvaton Dynamics

We compute the fully renormalized one-loop effective action for two interacting and self-interacting scalar fields in FRW space-time. We then derive and solve the quantum corrected equations of motion both for fields that dominate the energy density (such as an inflaton) and fields that do not (such as a subdominant curvaton). In particular, we introduce quantum corrected Friedmann equations that determine the evolution of the scale factor. We find that in general, gravitational corrections are negligible for the field dynamics. For the curvaton-type fields this leaves only the effect of the flat-space Coleman-Weinberg-type effective potential, and we find that these can be significant. For the inflaton case, both the corrections to the potential and the Friedmann equations can lead to behaviour very different from the classical evolution. Even to the point that inflation, although present at tree level, can be absent at one-loop order.

gr-qc↗