Cosmology with Higgs inflation

Cosmic inflation is a hypothetical period in the early universe, where the expansion of space accelerated. Inflation explains many properties of the observed universe, but its cause is not known. Higgs inflation is a model where inflation is caused by the Higgs field of the Standard Model of particle physics, coupled non-minimally to gravity. In this thesis, we study various aspects of cosmology with Higgs inflation. Inflation leaves marks on the cosmic microwave background radiation, and these marks can be used to distinguish inflationary models from each other. We study hilltop Higgs inflation, a model where quantum corrections produce a local maximum into the Higgs potential, and show that there the predicted tensor-to-scalar ratio is less than or equal to 1.2 × 10^-3. This is smaller than the prediction of tree-level Higgs inflation by a factor of four or more and can be probed by next-generation microwave telescopes. We also study reheating, the process where the universe transitions from inflation to radiation domination with a thermal bath of relativistic Standard Model particles. We show that in Higgs inflation, reheating is particularly efficient in the Palatini formulation of general relativity, because there Higgs bosons are produced violently by a tachyonic instability. The duration of reheating affects, for example, the predicted spectral index of the primordial perturbations. Finally, we discuss the production of primordial black holes in Higgs inflation. We show that large quantities of such black holes can be produced, but in order to satisfy observational constraints on large scales, they must be so small that they would have evaporated by now by Hawking radiation. However, if the evaporating black holes left behind Planck mass relics, these could constitute part or all of the dark matter, the dominant, unknown matter component of the universe. Together, these studies show that even though the ingredients that go into Higgs inflation are simple, they lead to a rich phenomenology and offer valuable insights into inflation, gravitational degrees of freedom and the origin of dark matter.Kosminen inflaatio on varhaisen maailmankaikkeuden hypoteettinen ajanjakso, jonka aikana avaruus laajeni kiihtyvästi. Inflaatio pystyy selittämään monet havaitun maailmankaikkeuden erityispiirteet, kuten sen laakeuden ja homogeenisuuden, mutta inflaation aiheuttaneesta mekanismista ei ole varmuutta. Higgsin inflaatiossa hiukkasmallin standardimallissa esiintyvä Higgsin kenttä aiheuttaa kosmisen inflaation. Tässä väitöskirjassa tutkitaan Higgsin inflaatioon liittyvän kosmologian erityispiirteitä. Inflaatio jättää kosmiseen mikroaaltotaustasäteilyyn jälkiä, joiden avulla erilaiset inflaatiomallit voidaan erottaa toisistaan. Väitöskirjassa tutkitaan erästä Higgsin inflaation erikoistapausta, mäenhuippuinflaatiota, jossa kvanttikorjaukset muodostavat Higgsin potentiaaliin paikallisen maksimin, ja lasketaan mikroaaltotaustasäteilyn ennustettu muoto tässä tapauksessa. Malli ennustaa taustasäteilystä mitattavalle tensori-skalaari-suhteelle arvon, joka on vähintään neljä kertaa pienempi kuin tavanomaisessa Higgsin inflaatiossa. Skalaari-tensori-suhdetta ei vielä ole kyetty mittaamaan, mutta ennusteita voidaan verrata tulevaisuuden taustasäteilyhavaintoihin. Väitöskirjassa tutkitaan myös siirtymää kosmisesta inflaatiosta kuumaan varhaiseen maailmankaikkeuteen ja osoitetaan, että siirtymäprosessi on erityisen tehokas yleisen suhteellisuusteorian Palatini-muotoilussa. Siirtymäprosessia hallitsee tällöin Higgsin potentiaalin takyoninen epävakaus, joka tuottaa nopeasti suuren määrän korkeaenergisiä Higgsin hiukkasia. Siirtymän nopeuden tunteminen on tärkeää, koska se vaikuttaa mallin antamiin taustasäteilyennusteisiin. Lopuksi väitöskirjassa tarkastellaan varhaisten mustien aukkojen tuottoa Higgsin inflaatiossa. Tällaisia mustia aukkoja voi syntyä inflaation seurauksena, ja ne voivat toimia havaittuna mutta toistaiseksi tuntemattomana pimeänä aineena. Higgsin inflaatio voi tuottaa suuren määrän mustia aukkoja, mutta kun havaitun mikroaaltotaustasäteilyn asettamat rajat otetaan huomioon, osoittautuu, että syntyvät mustat aukot ovat liian pieniä ollakseen pimeää ainetta — Hawkingin säteily haihduttaa ne nopeasti olemattomiin. Tältä vältytään, jos mustat aukot eivät haihdu täysin vaan jättävät jälkeensä Planckin massaisia jäänteitä. Tällaiset jäänteet voisivat muodostaa kaiken havaitun pimeän aineen. Kaiken kaikkiaan väitöskirjatutkimus osoittaa, että vaikka Higgsin inflaatiota varten tehdyt oletukset ovat yksinkertaisia, malli johtaa moniin mielenkiintoisiin ilmiöihin ja auttaa ymmärtämään kosmista inflaatiota, gravitaatioon liittyviä vapausasteita ja pimeän aineen alkuperää

Numerical stochastic inflation constrained by frozen noise

Stochastic inflation can resolve strong inflationary perturbations, which seed primordial black holes. I present a fast and accurate way to compute these perturbations in typical black hole producing single-field models, treating the short-wavelength Fourier modes beyond the de Sitter approximation. The squeezing and freezing of the modes reduces the problem to one dimension, and the resulting new form of the stochastic equations, dubbed `constrained stochastic inflation,' can be solved efficiently with semi-analytical techniques and numerical importance sampling. In an example case, the perturbation distribution is resolved in seconds deep into its non-Gaussian tail, a speed-up of factor $10^9$ compared to a previous study. Along the way, I comment on the role of the momentum constraint in stochastic inflation.Comment: 34 pages, 8 figures, 1 table. v2: Minor revisions in text. Published versio

Stochastic constant-roll inflation and primordial black holes

Stochastic inflation resolves primordial perturbations non-linearly, probing their probability distribution deep into its non-Gaussian tail. The strongest perturbations collapse into primordial black holes. In typical black-hole-producing single-field inflation, the strongest stochastic kicks occur during a period of constant roll. In this paper, I solve the stochastic constant-roll system, drawing the stochastic kicks from a numerically computed power spectrum, beyond the usual de Sitter approximation. The perturbation probability distribution is an analytical function of the integrated power spectrum $\sigma_k^2$ and the second slow-roll parameter $\epsilon_2$. With a large $\epsilon_2$, stochastic effects can reduce the height of the curvature power spectrum required to form asteroid mass black holes from $10^{-2}$ to $10^{-3}$. I compare these results to studies with the non-stochastic $\Delta N$ formalism.Comment: 10 pages, 3 figures, 1 tabl

Planck scale black hole dark matter from Higgs inflation

We study the production of primordial black hole (PBH) dark matter in the case when the Standard Model Higgs coupled non-minimally to gravity is the inflaton. PBHs can be produced if the Higgs potential has a near-critical point due to quantum corrections. In this case the slow-roll approximation may be broken, so we calculate the power spectrum numerically. We consider both the metric and the Palatini formulation of general relativity. Combining observational constraints on PBHs and on the CMB spectrum we find that PBHs can constitute all of the dark matter only if they evaporate early and leave behind Planck mass relics. This requires the potential to have a shallow local minimum, not just a critical point. The initial PBH mass is then below 10(6) g, and predictions for the CMB observables are the same as in tree-level Higgs inflation, n(s) = 0.96 and r = 5 x 10(-3) (metric) or r = 4 x 10(-8) ... 2 x 10(-7) (Palatini).Peer reviewe

Decoherence in Inflation

In this thesis, we study the decoherence of cosmological scalar perturbations during inflation. We first discuss the FRW model and cosmic inflation. Inflation is a period of accelerated expansion in the early universe, in typical models caused by a scalar field called inflaton. We review cosmological perturbation theory, where perturbations of the inflaton field and scalar degrees of freedom of the metric tensor are combined into the gauge-invariant Sasaki-Mukhanov variable. We quantize this variable using canonical quantization. Then, we discuss how interactions between the perturbations and their environment can lead to decoherence. In decoherence, the reduced density operator of the perturbations becomes diagonal with respect to a particular pointer basis. We argue that the pointer basis for the cosmological scalar perturbations consists of approximate eigenstates of the field value operator. Finally, we discuss how decoherence can help understand the transition from quantum theory to classical perturbation theory, and justify the standard treatment of perturbations and their initial conditions in cosmology. We conclude that since decoherence should not spoil the observationally successful predictions of this standard treatment, it is unlikely that the actual amount of decoherence could be observed in, say, the CMB radiation

Beyond (and back to) Palatini quadratic gravity and inflation

We study single-field slow-roll inflation embedded in Palatini $F(R)$ gravity where $F(R)$ grows faster than $R^2$. Surprisingly, the consistency of the theory requires the Jordan frame inflaton potential to be unbounded from below. Even more surprisingly, this corresponds to an Einstein frame inflaton potential bounded from below and positive definite. We prove that for all such Palatini $F(R)$'s, there exists a universal strong coupling limit corresponding to a quadratic $F(R)$ with the wrong sign for the linear term and a cosmological constant in the Jordan frame. In such a limit, the tensor-to-scalar ratio $r$ does not depend on the original inflaton potential, while the scalar spectral index $n_s$ does. Unfortunately, the system is ill-defined out of the slow-roll regime. A possible way out is to upgrade to a $F(R,X)$ model, with $X$ the Jordan frame inflaton kinetic term. Such a modification essentially leaves the inflationary predictions unaffected.Comment: 21 pages, 7 figures, revised version: added a section on $F(R,X)$ models, title, abstract and conclusions revise

Tachyonic Preheating in Palatini R2R^2 Inflation

We study preheating in the Palatini formalism with a quadratic inflaton potential and an added $\alpha R^2$ term. In such models, the oscillating inflaton field repeatedly returns to the plateau of the Einstein frame potential, on which the tachyonic instability fragments the inflaton condensate within less than an e-fold. We find that tachyonic preheating takes place when $\alpha \gtrsim 10^{13}$ and that the energy density of the fragmented field grows with the rate $\Gamma/H \approx 0.011 \times \alpha^{0.31}$. The model extends the family of plateau models with similar preheating behaviour. Although it contains non-canonical quartic kinetic terms in the Einstein frame, we show that, in the first approximation, these can be neglected during both preheating and inflation.Comment: Matches published versio

Gravitational dark matter production in Palatini preheating

We study preheating in plateau inflation in the Palatini formulation of general relativity, in a special case that resembles Higgs inflation. It was previously shown that the oscillating inflaton field returns to the plateau repeatedly in this model, and this leads to tachyonic production of inflaton particles. We show that a minimally coupled spectator scalar field can be produced even more efficiently by a similar mechanism. The mechanism is purely gravitational, and the scalar field mass can be of order $10^{13}$ GeV, larger than the Hubble scale by many orders of magnitude, making this a candidate for superheavy dark matter.Comment: Section 4 extended, references added, typos fixed, matches published versio

Critical point Higgs inflation in the Palatini formulation

We study Higgs inflation in the Palatini formulation with the renormalisation group improved potential in the case when loop corrections generate a feature similar to an inflection point. Assuming that there is a threshold correction for the Higgs quartic coupling lambda and the top Yukawa coupling y(t), we scan the three-dimensional parameter space formed by the two jumps and the non-minimal coupling xi .The spectral index n(s) can take any value in the observationally allowed range. The lower limit for the running is alpha (s)> -3.5 x 10(-3), and alpha (s) can be as large as the observational upper limit. Running of the running is small. The tensor-to-scalar ratio is 2.2x10(-17)< r < 2 x 10(-5). We find that slow-roll can be violated near the feature, and a possible period of ultra-slow-roll contributes to the widening of the range of CMB predictions. Nevertheless, for the simplest tree-level action, the Palatini formulation remains distinguishable from the metric formulation even when quantum corrections are taken into account, because of the small tensor-to-scalar ratio.Peer reviewe

Observable Gravitational Waves from Hyperkination in Palatini Gravity and Beyond

We consider cosmology with an inflaton scalar field with an additional quartic kinetic term. Such a theory can be motivated by Palatini $R+R^2$ modified gravity. Assuming a runaway inflaton potential, we take the Universe to become dominated by the kinetic energy density of the scalar field after inflation. Initially, the leading kinetic term is quartic and we call the corresponding period hyperkination. Subsequently, the usual quadratic kinetic term takes over and we have regular kination, until reheating. We study, both analytically and numerically, the spectrum of primordial gravitational waves generated during inflation and re-entering the horizon during the subsequent eras. We demonstrate that the spectrum is flat for modes re-entering during radiation domination and hyperkination and linear in frequency for modes re-entering during kination: kinetic domination boosts the spectrum, but hyperkination truncates its peak. As a result, the effects of the kinetic period can be extended to observable frequencies without generating excessive gravitational waves, which could otherwise destabilise the process of Big Bang Nucleosynthesis. We show that there is ample parameter space for the primordial gravitational waves to be observable in the near future. If observed, the amplitude and `knee' of the spectrum will provide valuable insights into the background theory.Comment: 40 pages, 7 figure