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@PHDTHESIS{Sagunski:307715,
      author       = {Sagunski, Laura},
      othercontributors = {Konstandin, Thomas and Sigl, Guenter},
      title        = {{O}n {S}oft {L}imits of {L}arge-{S}cale {S}tructure
                      {C}orrelation {F}unctions},
      issn         = {1435-8085},
      school       = {Universität Hamburg},
      type         = {Dissertation},
      address      = {Hamburg},
      publisher    = {Verlag Deutsches Elektronen-Synchrotron},
      reportid     = {PUBDB-2016-03361, DESY-THESIS-2016-023},
      series       = {DESY-THESIS},
      pages        = {247},
      year         = {2016},
      note         = {Dissertation, Universität Hamburg, 2016},
      abstract     = {Large-scale structure surveys have the potential to become
                      the leading probe for precision cosmology in the next
                      decade. To extract valuable information on the cosmological
                      evolution of the Universe from the observational data, it is
                      of major importance to derive accurate theoretical
                      predictions for the statistical large-scale structure
                      observables, such as the power spectrum and the bispectrum
                      of (dark) matter density perturbations. Hence, one of the
                      greatest challenges of modern cosmology is to theoretically
                      understand the non-linear dynamics of large-scale structure
                      formation in the Universe from first principles. While
                      analytic approaches to describe the large-scale structure
                      formation are usually based on the framework of
                      non-relativistic cosmological perturbation theory, we pursue
                      another road in this thesis and develop methods to derive
                      generic, non-perturbative statements about large-scale
                      structure correlation functions. We study unequal- and
                      equal-time correlation functions of density and velocity
                      perturbations in the limit where one of their wavenumbers
                      becomes small, that is, in the soft limit. In the soft
                      limit, it is possible to link
                      $\left(\mathcal{N}+1\right)$-point and $\mathcal{N}$-point
                      correlation functions to non-perturbative `consistency
                      conditions'. These provide in turn a powerful tool to test
                      fundamental aspects of the underlying theory at hand. In
                      this work, we first rederive the (resummed) consistency
                      conditions at unequal times by using the so-called eikonal
                      approximation. The main appeal of the unequal-time
                      consistency conditions is that they are solely based on
                      symmetry arguments and thus are universal. Proceeding from
                      this, we direct our attention to consistency conditions at
                      equal times, which, on the other hand, depend on the
                      interplay between soft and hard modes. We explore the
                      existence and validity of equal-time consistency conditions
                      within and beyond perturbation theory. For this purpose, we
                      investigate the predictions for the soft limit of the
                      bispectrum of density and velocity perturbations in two
                      different approaches, namely in the perturbative time-flow
                      approach and in a non-perturbative background method. This
                      background method, which relies on absorbing a spherically
                      symmetric soft mode into a locally curved background
                      cosmology, has recently inspired a proposal for an
                      (allegedly non-perturbative) angular-averaged equal-time
                      consistency condition for the bispectrum of density
                      perturbations (henceforth referred to as VKPR proposal). We
                      demonstrate explicitly for an Einstein-de Sitter universe
                      that the time-flow relations as well as the VKPR proposal
                      are only fulfilled at leading order in perturbation theory,
                      but are not exact beyond it. Since the VKPR proposal still
                      leads to qualitatively accurate predictions for the
                      bispectrum of density perturbations beyond the linear
                      perturbative order, it can nevertheless be regarded as a
                      reasonable empirical approximation in this case. However,
                      transferring the VKPR proposal to the velocity perturbations
                      significantly fails beyond linear order in perturbation
                      theory. In consequence, we generalize the background method
                      to properly account for the effect of local curvature both
                      in the density and velocity perturbations on short distance
                      scales. This allows us not only to identify the
                      discrepancies of the VKPR proposal, but also to formulate a
                      proper generalization of it which includes both the density
                      and velocity perturbations. In addition, we use the
                      background method to deduce a generic, non-perturbative
                      angular-averaged bispectrum consistency condition, which
                      depends on the density power spectrum of hard modes in the
                      presence of local curvature.Building upon this, we proceed
                      by deriving a non-perturbative equation for the power
                      spectrum in the soft limit. To this end, we perform an
                      operator product expansion, on the one hand, and deduce a
                      non-perturbative angular-dependent bispectrum consistency
                      condition, on the other hand. We obtain the latter from
                      extending the background method to the case of a directional
                      soft mode, being absorbed into a locally curved anisotropic
                      background cosmology. The resulting non-perturbative power
                      spectrum equation encodes the coupling to ultraviolet (UV)
                      modes in two time-dependent coefficients. These can most
                      generally be inferred from response functions to geometrical
                      parameters, such as spatial curvature, in the locally curved
                      anisotropic background cosmology. However, we can determine
                      one coefficient by use of the angular-averaged bispectrum
                      consistency condition together with the generalized VKPR
                      proposal, and we show that the impact of the other one is
                      subleading. Neglecting the latter in consequence, we
                      confront the non-perturbative power spectrum equation
                      against numerical simulations and find indeed a very good
                      agreement within the expected error bars. Moreover, we argue
                      that both coefficients and thus the non-perturbative power
                      spectrum in the soft limit depend only weakly on UV modes
                      deep in the non-linear regime. This non-perturbative finding
                      allows us in turn to derive important implications for
                      perturbative approaches to large-scale structure formation.
                      First, it leads to the conclusion that the UV dependence of
                      the power spectrum found in explicit computations within
                      standard perturbation theory is an artifact. Second, it
                      implies that in the Eulerian (Lagrangian) effective field
                      theory (EFT) approach, where UV divergences are canceled by
                      counter-terms, the renormalized leading-order coefficient(s)
                      receive most contributions from modes close to the
                      non-linear scale. The non-perturbative approach we developed
                      can in principle be used to precisely infer the size of
                      these renormalized leading-order EFT coefficient(s) by
                      performing small-volume numerical simulations within an
                      anisotropic `separate universe' framework. Our results
                      suggest that the importance of these coefficient(s) is a
                      $\sim 10 \\%$ effect at most.},
      cin          = {T},
      cid          = {I:(DE-H253)T-20120731},
      pnm          = {611 - Fundamental Particles and Forces (POF3-611) / PHGS,
                      VH-GS-500 - PIER Helmholtz Graduate School
                      $(2015_IFV-VH-GS-500)$},
      pid          = {G:(DE-HGF)POF3-611 / $G:(DE-HGF)2015_IFV-VH-GS-500$},
      experiment   = {EXP:(DE-MLZ)NOSPEC-20140101},
      typ          = {PUB:(DE-HGF)3 / PUB:(DE-HGF)11},
      doi          = {10.3204/PUBDB-2016-03361},
      url          = {https://bib-pubdb1.desy.de/record/307715},
}