Efektivna teorija polja formacije kozmoloških struktura

master's thesis

• Title (english): Effective field theory of cosmological structure formation
• Author: Ivan Sladoljev
• Mentor: Zvonimir Vlah (mentor)
• Mentor: Sanjin Benić (komentor)
• Committee member: Sanjin Benić (predsjednik povjerenstva)
• Committee member: Zvonimir Vlah (član povjerenstva)
• Committee member: Krešimir Kumerički (član povjerenstva)
• Committee member: Davor Horvatić (član povjerenstva)
• Committee member: Ivica Smolić (član povjerenstva)
• Granter: University of Zagreb; Faculty of Science; (Department of Physics); Zagreb
• Defense date and country: 2024-02-29, Croatia
• Scientific / art field, discipline and subdiscipline: NATURAL SCIENCES; Physics

Abstract

Postoje mnoge dobre teorije za opisivanje evolucije polja materije na velikim udaljenostima te postupni nastanak struktura kozmičke mreže. Najpoznatija od njih je standardna perturbacijska teorija (SPT), koja razvija polje kontrasta materije δ(x, t) u red po faktoru skale a(t) te perturbativnim pristupom opisuje dinamiku nastanka struktura na velikim skalama. Ovakav razvoj dobro opisuje spektar snage na velikim skalama (r ≈ 100 Mpc) te neke od nelinearnih pojava, poput širenja i pomicanja BAO vrha [23]. No veliki problem takvog pristupa jest da ispod r ≈ 10 Mpc [21] interakcija različitih modova polja materije postaje nelinearna te je nemoguće precizno primijeniti perturbacijsku teoriju. Stoga ćemo u ovom radu proučavati efektivne perturbacijske teorije. Posebno ćemo se fokusirati na Eulerovu (EFTLSS) i Lagrangeovu (LEFTLSS) efektivnu perturbacijsku teoriju te ćemo pokazati kako integracijom preko dinamike malih (nelinearnih) skala dobivamo puno preciznije predikcije za spektar snage na velikim skalama. Na početku ćemo detaljno izvesti jednadžbe i rješenja dva klasična perturbacijska pristupa, odnosno standardne (SPT) i Lagrangeove (LPT) perturbacijske teorije. Također ćemo pokazati ekvivalenciju njihovih rješenja, odnosno da n-ti red SPT-a konvergira LPT Zeldovich aproksimaciji. Cjelokupne izvode radit ćemo u jednoj dimenziji što nam, osim egzaktnosti konačnog rješenja, omogućuje lakšu numeričku provjeru rezultata. Bitno je za naglasiti kako radom u jednoj dimenziji možemo reproducirati sve predikcije 3D teorija. Usporedbom dobivenih izvoda perturbacijskih teorija s rješenjem numeričkih simulacija pokazat ćemo kako SPT i LPT loše aproksimiraju nelinearni spektar snage tamne materije. Nakon toga ćemo uvesti efektivni formalizam tih teorija te pokazati kako filtriranjem višim mome nata Vlasovljeve jednadžbe dobivamo preciznija rješenja za nelinearni spektar snage. Rješavajući dinamičke jednadžbe koje ovise samo o uglađenim poljima izvest ćemo puni 1 − loop spektar te sve slobodne parametre i protučlanove. Pokazat ćemo kako tim slobodnim parametrima možemo modelirati male skale preko kojih smo filtrirali i na taj način bolje opisati dinamiku na velikim skalama. Fokusirat ćemo se i na ovisnosti tih parametara o skali preko koje filtriramo, kao i pokazati način određivanja efektivnih parametara direktno iz teorije. Cilj ovog rada jest pokazati bolji način modeliranja spektra snage za razvoj velikih struktura te pokazati kako radom u jednoj dimenziji možemo brže i lakše doći do istih rezultata kao i u 3D.

Abstract (english)

We have a good understanding of the cosmic dynamics that govern the evolution of matter on large scales. But on scales smaller than 10 Mpc, due to the extremely nonlinear nature of the interactions, many of our best theories for modeling Large Scale Structures (such as the Eulerian standard perturbation theory (SPT)) have had trouble describing the precise evolution of matter density fields. The biggest problem of SPT is that it treats all scales as if they were pertubative, even if they’re not. This warrants a new approach for probing into the small scale dynamics of matter fields and subsequent formation of the Large Scale Structures. In this thesis we will tackle those problems by looking at Lagrangian and Eulerian effective perturbation theories, that had recent success in tackling these problems by filtering out small scale behaviour and modeling it with new free parameters. We will be working in a simplified 1D case of gravitationally interacting sheets, to reduce the number of calculations needed but still show all the important behaviors as in 3D. In this thesis, we will firstly derive the full standrard Lagrangian and Eulerian formulation and show that the nth-order Eulerian perturbation theory converges to the Zeldovich approximation (linear order LPT) as n → ∞, although this is only true for linear scales up to shell crossing. We will also show how LPT and SPT fails to recover the true nonlinear power spectrum calculated thorugh numerical simulations. We will then focus heavily on effective formulation in Eulerian and Lagrangian space. We will fully derive the 1-loop extensions of both the EFT and LFT by smoothing the higher multipole moments of Vlasov’s equation. By using dynamical equations that depend only on smoothed fields with small RMS, we will show how they describe the dynamics on large scales better than standard theories. We will also derive all the counterterms and free parameters, tackle their cutoff dependency and show how to extended the range over which perturbation theory is percent-level accurate. The goal is to show that 1D solutions are interesting to study as they yield the same result as in 3D, with considerably simplified derivations.

• Keywords: SPT; LPT; efektivna teorija polja; strukture na velikim skalama
• Keywords (english): Large Scale Structure; SPT; LPT; effective field theory
• Language: croatian
• URN:NBN: urn:nbn:hr:217:266709
• Study programme: Title: The University Integrated Undergraduate and Graduate Programme in Physics; Research Physics; specializations in: Research Physics; Course: Research Physics; Study programme type: university; Study level: integrated undergraduate and graduate; Academic / professional title: sveučilišni magistar fizike (sveučilišni magistar fizike)
• Type of resource: Text
• File origin: Born digital
• Access conditions: Open access
• Created on: 2024-04-05 12:28:41