arXiv subjects

Jakub Mielczarek

Publications and source records attributed to Jakub Mielczarek.

71 records · Page 4Linked to original sources

arXiv2010

Vortex in axion condensate as a dark matter halo

We study the possibility of the vortices formation in axion condensate on the galactic scale. Such vortices can occur as a result of global rotation of the early universe. We study analytical models of vortices and calculate exemplary galaxy rotation curves. Depending on the setup it is possible to obtain a variety of shapes which give a good qualitative agreement with observational results. However, as we show, the extremely low velocity dispersions of the axions velocity are required to form the single vortex on the galactic scales. We find that the required velocity dispersion is of the order of $σ\approx 10^{-12} \frac{m}{s}$. This is much smaller that predicted within the present understanding of the axion physics. The vortices in axion condensate can be however formed on the much smaller scales and give seeds to the galaxy formation and to their angular momenta. On the other hand, the vortices can be formed on the galactic scales, but only if the mass of the axion-like particles is of the order of $10^{-30}$eV. In this case, the particle de Broglie wavelength is comparable with the galactic diameter. This condition must be fulfilled in order to keep the coherence of the quantum condensate on the galactic scales.

astro-ph↗

arXiv2010

Observables for FRW model with cosmological constant in the framework of loop cosmology

We consider a flat cosmological model with a free massless scalar field and the cosmological constant $Λ$ in the framework of loop quantum cosmology. The scalar field plays the role of an intrinsic time. We apply the reduced phase space approach. The dynamics of the model is solved analytically. We identify elementary observables and their algebra. The compound physical observables like the volume and the energy density of matter field are analysed. Both compound observables are bounded and oscillate in the $Λ<0$ case. The energy density is bounded and oscillates in the $Λ>0$ case. However, the volume is unbounded from above, but periodic. The difference between standard and nonstandard loop quantum cosmology is described.

gr-qc↗

arXiv2010

Inflation in loop quantum cosmology: Dynamics and spectrum of gravitational waves

Loop quantum cosmology provides an efficient framework to study the evolution of the Universe beyond the classical Big Bang paradigm. Because of holonomy corrections, the singularity is replaced by a "bounce". The dynamics of the background is investigated into the details, as a function of the parameters of the model. In particular, the conditions required for inflation to occur are carefully considered and are shown to be generically met. The propagation of gravitational waves is then investigated in this framework. By both numerical and analytical approaches, the primordial tensor power spectrum is computed for a wide range of parameters. Several interesting features could be observationally probed.

gr-qc↗

arXiv2010

Observational hints on the Big Bounce

In this paper we study possible observational consequences of the bouncing cosmology. We consider a model where a phase of inflation is preceded by a cosmic bounce. While we consider in this paper only that the bounce is due to loop quantum gravity, most of the results presented here can be applied for different bouncing cosmologies. We concentrate on the scenario where the scalar field, as the result of contraction of the universe, is driven from the bottom of the potential well. The field is amplified, and finally the phase of the standard slow-roll inflation is realized. Such an evolution modifies the standard inflationary spectrum of perturbations by the additional oscillations and damping on the large scales. We extract the parameters of the model from the observations of the cosmic microwave background radiation. In particular, the value of inflaton mass is equal to $m=(2.6 \pm 0.6) \cdot 10^{13}$ GeV. In our considerations we base on the seven years of observations made by the WMAP satellite. We propose the new observational consistency check for the phase of slow-roll inflation. We investigate the conditions which have to be fulfilled to make the observations of the Big Bounce effects possible. We translate them to the requirements on the parameters of the model and then put the observational constraints on the model. Based on assumption usually made in loop quantum cosmology, the Barbero-Immirzi parameter was shown to be constrained by $γ<1100$ from the cosmological observations. We have compared the Big Bounce model with the standard Big Bang scenario and showed that the present observational data is not informative enough to distinguish these models.

gr-qc↗

arXiv2009

Asymmetric cyclic evolution in polymerised cosmology

The dynamical systems methods are used to study evolution of the polymerised scalar field cosmologies with the cosmological constant. We have found all evolutional paths admissible for all initial conditions on the two-dimensional phase space. We have shown that the cyclic solutions are generic. The exact solution for polymerised cosmology is also obtained. Two basic cases are investigated, the polymerised scalar field and the polymerised gravitational and scalar field part. In the former the division on the cyclic and non-cyclic behaviour is established following the sign of the cosmological constant. The value of the cosmological constant is upper bounded purely from the dynamical setting.

gr-qc↗

arXiv2009

Smoothed quantum fluctuations and CMB observations

In this paper we investigate power spectrum of a smoothed scalar field. The smoothing leads to the regularisation of the UV divergences and can be related with the internal structure of the considered field or the space itself. We apply procedure of smoothing to the quantum fluctuations generated during the phase of cosmic inflation. We study whether this effect can be probed observationally and conclude that the modifications of the power spectrum due to the smoothing on the Planck scale are negligible and far beyond the observational abilities. Subsequently we investigate whether smoothing in any other form can be probed observationally. We introduce phenomenological smoothing factor $e^{-k^2σ^2}$ to the inflationary spectrum and investigate its effects on the spectrum of CMB anisotropies and polarisation. We show that smoothing can lead to suppression of high multipoles in the spectrum of the CMB. Based on five years observations of WMAP satellite we indicate that the present scale of high multipoles suppression is constrained by $σ< 2.86$ Mpc (95% CL). This corresponds to the constraint $σ< 100 μ$m at the end of inflation. Despite this value is far above the Planck scale, the other processes of smoothing can be possibly studied with this constraint, e.g. diffusion or decoherence of primordial perturbations.

hep-th↗

arXiv2009

The Observational Implications of Loop Quantum Cosmology

In this paper we consider realistic model of inflation embedded in the framework of loop quantum cosmology. Phase of inflation is preceded here by the phase of a quantum bounce. We show how parameters of inflation depend on the initial conditions established in the contracting, pre-bounce phase. Our investigations indicate that phase of the bounce easily sets proper initial conditions for the inflation. Subsequently we study observational effects that might arise due to the quantum gravitational modifications. We perform preliminary observational constraints for the Barbero-Immirzi parameter $γ$, critical density $ρ_{\text{c}}$ and parameter $λ$. In the next step we study effects on power spectrum of perturbations. We calculate spectrum of perturbations from the bounce and from the joined bounce+inflation phase. Based on these studies we indicate possible way to relate quantum cosmological models with the astronomical observations. Using the Sachs-Wolfe approximation we calculate spectrum of the super-horizontal CMB anisotropies. We show that quantum cosmological effects can, in the natural way, explain suppression of the low CMB multipoles. We show that fine-tuning is not required here and model is consistent with observations. We also analyse other possible probes of the quantum cosmologies and discuss perspectives of their implementation.

gr-qc↗

arXiv2009

Effective dynamics of the closed loop quantum cosmology

In this paper we study dynamics of the closed FRW model with holonomy corrections coming from loop quantum cosmology. We consider models with a scalar field and cosmological constant. In case of the models with cosmological constant and free scalar field, dynamics reduce to 2D system and analysis of solutions simplify. If only free scalar field is included then universe undergoes non-singular oscillations. For the model with cosmological constant, different behaviours are obtained depending on the value of $Λ$. If the value of $Λ$ is sufficiently small, bouncing solutions with asymptotic de Sitter stages are obtained. However if the value of $Λ$ exceeds critical value $Λ_{\text{c}} =\frac{\sqrt{3}m^2_{\text{Pl}}}{2πγ^3} \simeq 21 m^2_{\text{Pl}}$ then solutions become oscillatory. Subsequently we study models with a massive scalar field. We find that this model possess generic inflationary attractors. In particular field, initially situated in the bottom of the potential, is driven up during the phase of quantum bounce. This subsequently leads to the phase of inflation. Finally we find that, comparing with the flat case, effects of curvature do not change qualitatively dynamics close to the phase of bounce. Possible effects of inverse volume corrections are also briefly discussed.

gr-qc↗

arXiv2009

Effects of the quantisation ambiguities on the Big Bounce dynamics

In this paper we investigate dynamics of the modified loop quantum cosmology models using dynamical systems methods. Modifications considered come from the choice of the different field strength operator $\hat{F}$ and result in different forms of the effective Hamiltonian. Such an ambiguity of the choice of this expression from some class of functions is allowed in the framework of loop quantisation. Our main goal is to show how such modifications can influence the bouncing universe scenario in the loop quantum cosmology. In effective models considered we classify all evolutional paths for all admissible initial conditions. The dynamics is reduced to the form of a dynamical system of the Newtonian type on a 2-dimensional phase plane. These models are equivalent dynamically to the FRW models with the decaying effective cosmological term parametrised by the canonical variable $p$ (or by the scale factor $a$). We find that for the positive cosmological constant there is a class of oscillating models without the initial and final singularities. The new phenomenon is the appearance of curvature singularities for the finite values of the scale factor, but we find that for the positive cosmological constant these singularities can be avoided. For the positive cosmological constant the evolution begins at the asymptotic state in the past represented by the deSitter contracting (deS$_{-}$) spacetime or the static Einstein universe H=0 or $H=-\infty$ state and reaches the deSitter expanding state (deS$_{+}$), the state H=0 or $H=+\infty$ state. In the case of the negative cosmological constant we obtain the past and future asymptotic states as the Einstein static universes.

gr-qc↗

arXiv2009

Multi-fluid potential in the loop cosmology

The scalar field can behave like a fluid with equation of state $p_ϕ=wρ_ϕ$, where $w \in [-1,1]$. In this Letter we derive a class of the scalar field potentials for which $w=$ const. Scalar field with such a potential can mimic ordinary matter, radiation, cosmic strings, etc. We perform our calculations in the framework of the loop cosmology with holonomy corrections. We solve the model analytically for the whole parameter space. Subsequently, we perform similar consideration for the model with a phantom field ($w<-1$). We show that scalar field is monotonic function in both cases. This indicates that it can be treated as a well-defined internal time for these models. Moreover we perform preliminary studies of the scalar field perturbations with this potential. We indicate that non-Gaussian features are present admitting for the possible observational constraints of the model.

gr-qc↗

arXiv2009

Tensor power spectrum with holonomy corrections in LQC

In this paper we consider tensor perturbations produced at a bounce phase in presence of the holonomy corrections. Here bounce phase and holonomy corrections originate from Loop Quantum Cosmology. We re-derive formulas for the corrections for the model with a scalar field content. Background dynamics with a free scalar field and multi-fluid potential are considered. Since the considerations are semi-classical effects of quantum fluctuations of the background dynamics are not taken into account. Quantum and classical back-reaction effects are also neglected. To find spectrum of the gravitational waves both analytical approximations as well as numerical investigations were performed. We have found analytical solutions on super-horizontal and sub-horizontal regimes and derived corresponding tensor power spectra. Also occupation number $n_{\bf k}$ and parameter $Ω_{\text{gw}}$ were derived in sub-horizontal limit, leading to its extremely low present value. Final results are numerical power spectra of the gravitational waves produced in presence of quantum holonomy corrections. The obtained spectrum has two UV and IR branches where $\mathcal{P}_T \propto k^2$, however with the different prefactors. Spectrum connecting these regions is in the form of oscillations. We have found good agreement between numerical spectrum and this obtained from the analytical model. Obtained spectrum can be directly applied as initial conditions for the inflationary modes. We mention possible resulting observational features of the CMB in particular B-type polarization.

gr-qc↗

arXiv2008

Universe from vacuum in loop-string cosmology

In this paper we study the description of the Universe based on the low energy superstring theory modified by the Loop Quantum Gravity effects.This approach was proposed by De Risi et al. in the Phys. Rev. D {\bf 76} (2007) 103531. We show that in the contrast with the string motivated pre-Big Bang scenario, the cosmological realisation of the $t$-duality transformation is not necessary to avoid an initial singularity. In the model considered the universe starts its evolution in the vacuum phase at time $t\to - \infty$. In this phase the scale factor $a\to 0$, energy density $ρ\to 0$ and coupling of the interactions $g^2_s \to 0$. After this stage the universe evolves to the non-singular hot Big Bang phase $ρ\to ρ_{\text{max}} < \infty$. Then the standard classical universe emerges. During the whole evolution the scale factor increases monotonically. We solve this model analytically. We also propose and solve numerically the model with an additional dilaton potential in which the universe starts the evolution from the asymptotically free vacuum phase $g^2_s \to 0$ and then evolves non-singularly to the emerging dark energy dominated phase with the saturated coupling constant $g^2_s \to \text{const}$.

hep-th↗

arXiv2008

Gravitational waves from the Big Bounce

In this paper we investigate gravitational waves production during the Big Bounce phase inspired by the Loop Quantum Cosmology. We consider the influence of the holonomy corrections to the equation for tensor modes. We show that they act like additional effective graviton mass, suppressing gravitational waves creation. However, this effects can be treated perturbatively. We investigate the simplified model without these corrections and find its exact analytical solution. For this model we calculate a spectrum of the gravitational waves from the Big Bounce phase. The obtained spectrum decreases to zero for the low energy modes. Based on this observation we indicate that this effect can lead to the low CMB multipoles suppression and gives a potential way to test Loop Quantum Cosmology models. We also consider a scenario with a post-bounce inflationary phase. The obtained power spectrum gives qualitative explanation of the CMB spectra, including low multipoles suppression. This result is a challenge to construct a consistent bounce+inflation model in the Loop Quantum Cosmology.

gr-qc↗

arXiv2008

Exact solutions for Big Bounce in loop quantum cosmology

In this paper we study the flat (k=0) cosmological FRW model with holonomy corrections of Loop Quantum Gravity. The considered universe contains a massless scalar field and the cosmological constant Lambda. We find analytical solutions for this model in different configurations and investigate its dynamical behaviour in the whole phase space. We show the explicit influence of Lambda on the qualitative and quantitative character of solutions. Even in the case of positive Lambda the oscillating solutions without the initial and final singularity appear as a generic case for some quantisation schemes.

gr-qc↗

arXiv2008

Emerging singularities in the bouncing loop cosmology

In this paper we calculate $\mathcal{O}(μ^4)$ corrections from holonomies in the Loop Quantum Gravity, usually not taken into account. Allowance of the corrections of this kind is equivalent with the choice of the new quatization scheme. Quantization ambiguities in the Loop Quantum Cosmology allow for this additional freedom and presented corrections are consistent with the standard approach. We apply these corrections to the flat FRW cosmological model and calculate the modified Friedmann equation. We show that the bounce appears in the models with the standard $\mathcal{O}(μ^2)$ quantization scheme is shifted to the higher energies $ρ_{\text{bounce}} = 3 ρ_{\text{c}}$. Also a pole in the Hubble parameter appears for $ρ_{\text{pole}} = {3/2} ρ_{\text{c}}$ corresponding to \emph{hyper-inflation/deflation} phases. This pole represents a curvature singularity at which the scale factor is finite. In this scenario the singularity and bounce co-exist. Moreover we find that an ordinary bouncing solution appears only when quantum corrections in the lowest order are considered. Higher order corrections can lead to the nonperturbative effects.

gr-qc↗

arXiv2007

Relic gravitons from super-inflation

The super-inflationary phase is predicted by the Loop Quantum Cosmology. In this paper we study the creation of gravitational waves during this phase. We consider the inverse volume corrections to the equation for the tensor modes and calculate the spectrum of the produced gravitons. The amplitude of the obtained spectrum as well as maximal energy of gravitons strongly depend on the evolution of the Universe after the super-inflation. We show that a further standard inflationary phase is necessary to lower the amount of gravitons below the present bound. In case of the lack of the standard inflationary phase, the present intensity of gravitons would be extremely large. These considerations give us another motivation to introduce the standard phase of inflation.

gr-qc↗

arXiv2007

Relic gravitons as the observable for Loop Quantum Cosmology

In this paper we investigate tensor modes of perturbations in the universe governed by Loop Quantum Cosmology. We derive the equation for tensor modes and investigate numerically effects of quantum corrections. This investigation reveals that the region of super-adiabatic amplification of tensor modes is smaller in comparison with the classical case. Neglecting quantum corrections to the equation for tensor modes and holding underlying loop dynamics we study analytically the creation of gravitons. We calculate the power spectrum of tensor perturbations during the super-inflationary phase induced by Loop Quantum Gravity. The main result obtained is the spectrum of gravitons, produced in the transition from the quantum to classical regime of the Universe. Obtained spectrum is characterized by a hard branch. The numerical investigation shows the strong dependence of $ν_{\text{max}}$ frequency with respect to quantum numbers. The parameter $Ω_{\text{gw}}(ν_{\text{max}})$ approaches even to $\sim 10^{-1}$ for highest frequencies. We compare our results with recent constraints from the Laser Interferometer Gravitational-wave Observatory (LIGO) and find that it is possible to test the quantum effects in the early Universe.

gr-qc↗