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Agradecimentos: This research was funded by FAPESP grants number 2016/13803-2 (D.D.C.), 2016/24029-6 (M.L.), 2017/05685-2 (all), 2018/01245-0 (T.N.dS.) and 2018/07833-1(M.H.). D.D.C., M.L., J.N., and J.T. thank CNPq for financial support. We also acknowledge computing time provided by the Research Computing Support Group at Rice University through agreement with the University of São Paulo Abstract: We propose a redefinition of the principal component analysis (PCA) of anisotropic flow that makes it more directly connected to fluctuations of the initial geometry of the system. Then, using state-of-the-art hydrodynamic simulations, we make an explicit connection between flow fluctuations and a cumulant expansion of the initial transverse geometry. In particular, we show that the second principal component of elliptic flow is generated by higher-order cumulants, and therefore probes smaller length scales of the initial state. With this information, it will be possible to put new constraints on properties of the early-time dynamics of a heavy-ion collision, including small-scale structure, as well as properties of the quark-gluon plasma FUNDAÇÃO DE AMPARO À PESQUISA DO ESTADO DE SÃO PAULO - FAPESP CONSELHO NACIONAL DE DESENVOLVIMENTO CIENTÍFICO E TECNOLÓGICO - CNPQ Fechado

Agradecimentos: We thank J.-F. Paquet, A. Mazeliuaskas, and Soeren Schlichting for help with the technical numerical aspects within KøMPøST and for comments on a preliminary version of this manuscript. This research was funded by FAPESP Grants No. 2016/13803-2 (D.D.C.), No. 2016/24029-6, No. 2018/24720-6 (M.L.), No. 2017/05685-2 (all), No. 2018/01245-0 (T.N.dS.), and No. 2018/07833-1 (M.H.). D.D.C., M.L., G.S.D., and J.T. thank CNPq for financial support. G.S.D. acknowledges financial support from Fundação Carlos Chagas Filho de Amparo à Pesquisa do Estado do Rio de Janeiro (FAPERJ), Grant No. E-26/202.747/2018. J.N. is partially supported by the US Department of Energy, Office of Science, Office for Nuclear Physics under Award No. DE-SC0021301. The authors also acknowledge computing time provided by the Research Computing Support Group at Rice University through agreement with the Universidade de São Paulo Abstract: We investigate the effects of prehydrodynamic evolution on final-state observables in heavy-ion collisions using state-of-the art event simulations coupled to different prehydrodynamic scenarios, which include the recently developed effective kinetic transport theory evolution model Kempty setMPempty setST. Differential flow observables are found to be mostly insensitive to the details of prehydrodynamic evolution. The main effect we observe is in the P T spectra, particularly the mean transverse momentum. However, at least part of this effect is a consequence of the underlying conformal invariance assumption currently present in such approaches, which is known to be violated in the temperature regime probed in heavy-ion collisions. This assumption of early time conformal invariance leads to an artificially large out-of-equilibrium bulk pressure when switching from (conformal) prehydrodynamic evolution to hydrodynamics (using the nonconformal QCD equation of state), which in turn increases the transverse momentum. Our study indicates that a consistent treatment of prehydrodynamic evolution in heavy-ion collisions requires the use of nonconformal models of early time dynamics FUNDAÇÃO DE AMPARO À PESQUISA DO ESTADO DE SÃO PAULO - FAPESP CONSELHO NACIONAL DE DESENVOLVIMENTO CIENTÍFICO E TECNOLÓGICO - CNPQ FUNDAÇÃO CARLOS CHAGAS FILHO DE AMPARO À PESQUISA DO ESTADO DO RIO DE JANEIRO - FAPERJ Fechado

Agradecimentos: We are thankful to D. Teaney, A. Mazeliauskas, S. Mohapatra, P. Bozek, and Marcus Bleicher for fruitful discussions. This research was funded by FAPESP Grants No. 2016/13803-2 (D.D.C.), No. 2016/24029-6 (M.L.), No. 2017/05685-2 (all), No. 2018/01245-0 (T.N.dS.), and No. 2018/07833-1(M.H.). D.D.C., M.L., J.N., and J.T. thank CNPq for financial support. We also acknowledge computing time provided by the Research Computing Support Group at Rice University through agreement with the University of São Paulo Abstract: In heavy-ion collisions, momentum-dependent pair correlations can be characterized by a principal component analysis (PCA), in which subleading modes are expected to reveal new information on flow fluctuations. However, we find that, as currently measured, these modes can be dominated by multiplicity fluctuations, which serve as an unwanted background. Here, we propose new PCA observables that are robust against multiplicity fluctuations and isolate novel sources of flow fluctuations, thus being suited to provide fresh insight into the initial stages of the system at small length scales FUNDAÇÃO DE AMPARO À PESQUISA DO ESTADO DE SÃO PAULO - FAPESP CONSELHO NACIONAL DE DESENVOLVIMENTO CIENTÍFICO E TECNOLÓGICO - CNPQ Fechado

Agradecimentos: We are thankful to G. S. Denicol, D. Teaney, and A. Mazeliauskas for fruitful discussions. This research was funded by FAPESP Grants No. 2016/13803-2 (D.D.C.), No. 2016/24029-6 (M.L.), No. 2017/05685-2 (all), No. 2018/01245-0 (T.N.dS.), No. 2018/07833-1 (M.H.), and No. 2019/16293-3 (J.G.P.B.). D.D.C., M.L., and J.T. thank CNPq for financial support. J.N. is partially supported by the U.S. Department of Energy, Office of Science, Office for Nuclear Physics under Award No. DE-SC0021301. This research used the computing resources and assistance of the John David Rogers Computing Center (CCJDR) in the Institute of Physics "Gleb Wataghin," University of Campinas Abstract: The connection between initial-state geometry and anisotropic flow can be quantified through a well-established mapping between P-T-integrated flow harmonics and cumulants of the initial transverse energy distribution. In this paper we successfully extend this mapping to also include P-T-differential flow. In doing so, we find that subleading principal components of anisotropic flow can reveal previously unobserved details of the hydrodynamic response, in both the linear and the nonlinear regimes. Most importantly, we show that they provide novel information on the small-scale structures present in the initial stage of relativistic heavy-ion collisions FUNDAÇÃO DE AMPARO À PESQUISA DO ESTADO DE SÃO PAULO - FAPESP CONSELHO NACIONAL DE DESENVOLVIMENTO CIENTÍFICO E TECNOLÓGICO - CNPQ Fechado