How to obtain a heavier math font?

Question

The current question is a follow-up to some previously asked questions, like this: It is possible to make fonts appear heavier (darker) in pdf output of Latex? and this: Make entire document heavier using pdfrender and this: Fake bold in LuaLaTeX. All of these questions deal with the document as a whole (equally text and math). In my case, I need to make only math font a bit thicker (darker). I use times for text and CM for math. The former is much heavier than the latter and they just look horrible. My goal then is to make CM math a little bit darker to shorten that gap. Is there a way to fix this? Thank you.

EDIT:

I add a not-so-minimal working example here showing my real usage as asked by some commentators. I use MiKTeX on Windows and I run pdflatex directly to obtain a pdf file:

\documentclass[a4paper,oneside,12pt,table]{book}
\usepackage[T1]{fontenc}
\usepackage{amsmath,amssymb,amsfonts}
\usepackage{textcomp}
\renewcommand{\rmdefault}{ptm}
\usepackage[scaled=0.92]{helvet}

\usepackage{pdfpages}
\usepackage{csquotes} 
\MakeOuterQuote{"}
\usepackage{moresize}
\usepackage{caption}
\usepackage[indention=10pt,position=top,margin=0pt,font=small,
            labelformat=parens,labelsep=space,skip=6pt,hypcap=false,
            labelfont=bf,list=true,textfont=sf]
            {subcaption}
\usepackage{graphicx,rotating,setspace}
\usepackage{array,booktabs,calc,longtable}
\usepackage{xcolor,multirow}
\usepackage{tocbibind}  % Show all lot, lof, loa, refs. in TOC
\usepackage{tikz}
\usetikzlibrary{calc}
\usepackage{microtype}
\usepackage[colorlinks=false, pdfborder={0 0 0}]{hyperref}
\usepackage{cleveref}

\usepackage{fancyhdr}
\pagestyle{fancy}
\fancyhf{}
\addtolength{\headheight}{2.5pt}
\lhead{\itshape \chaptername ~\thechapter}
\rhead{\itshape \leftmark}
\renewcommand{\chaptermark}[1]{\markboth{#1}{}}% remove "Chapter N." prefix
\cfoot{\thepage}
\renewcommand{\contentsname}{Table of Contents}
\renewcommand{\bibname}{References}

\begin{document}
\begin{titlepage}
Title Here and authorship
\end{titlepage}
\frontmatter
\pagestyle{plain}
\chapter{Dedication}
\chapter{Acknowledgments}
\chapter{Abstract}
\clearpage
  {%
    \singlespacing 
    \tableofcontents 
  }%
\clearpage
%========================= List of Figures ============================= 
\listoffigures
\clearpage
%=========================== List of Tables ============================ 
\listoftables 
\clearpage
%======================= List of Abbreviations ========================= 
\chapter{List of Abbreviations}
\clearpage
%================================ List of Symbols======================= 
\chapter{List of Symbols}
\clearpage
%================================ Main Chapters ======================== 
\pagestyle{fancy}
\mainmatter
\chapter{Introduction}
\section{First Section}
Some text which is OK! and some math which is so light:

\begin{equation}\label{e:barwq}
\begin{split}
H_c &=\frac{1}{2n} \sum^n_{l=0}(-1)^{l}(n-{l})^{p-2}
\sum_{l _1+\dots+ l _p=l}\prod^p_{i=1} \binom{n_i}{l _i}\\
&\quad\cdot[(n-l )-(n_i-l _i)]^{n_i-l _i}\cdot
\Bigl[(n-l )^2-\sum^p_{j=1}(n_i-l _i)^2\Bigr].
\end{split}
\end{equation}

%========================== Additonal Appendices ======================= Appendices
\appendix
\clearpage
%====================== References Section ============================= 
\setstretch{1}
\begin{thebibliography}{199} % 199 is a random guess of the total number of references
\end{thebibliography}

\end{document}

Answer 1

Comptuer Modern is intentionally light. It is better to choose a math font corresponding to your main text.

There is a package mathptmx in the psnfss bundle that sets the main text to ptm and fakes some corresponding math fonts. Using this gives better results than you are seeing. However, better would be to switch to a more modern solution provided by the newtxtext and newtxmath packages. Below are examples of each.

mathptmx

\documentclass[a4paper,oneside,12pt,table]{book}

\usepackage[T1]{fontenc}
\usepackage{amsmath,amssymb,amsfonts}
\usepackage{textcomp}
\usepackage{mathptmx}
\usepackage[scaled=0.92]{helvet}
\usepackage{microtype}

\begin{document}
\chapter{Introduction}
\section{First Section}
Some text which is OK! and some math which is the same weight:

\begin{equation}\label{e:barwq}
\begin{split}
H_c &=\frac{1}{2n} \sum^n_{l=0}(-1)^{l}(n-{l})^{p-2}
\sum_{l _1+\dots+ l _p=l}\prod^p_{i=1} \binom{n_i}{l _i}\\
&\quad\cdot[(n-l )-(n_i-l _i)]^{n_i-l _i}\cdot
\Bigl[(n-l )^2-\sum^p_{j=1}(n_i-l _i)^2\Bigr].
\end{split}
\end{equation}

\end{document}

newtxtext with newtxmath

\documentclass[a4paper,oneside,12pt,table]{book}

\usepackage[T1]{fontenc}
\usepackage[helvratio=0.92]{newtxtext}
\usepackage{newtxmath}
\usepackage{microtype}

\begin{document}
\chapter{Introduction}
\section{First Section}
Some text which is OK! and some math which is the same weight:

\begin{equation}\label{e:barwq}
\begin{split}
H_c &=\frac{1}{2n} \sum^n_{l=0}(-1)^{l}(n-{l})^{p-2}
\sum_{l _1+\dots+ l _p=l}\prod^p_{i=1} \binom{n_i}{l _i}\\
&\quad\cdot[(n-l )-(n_i-l _i)]^{n_i-l _i}\cdot
\Bigl[(n-l )^2-\sum^p_{j=1}(n_i-l _i)^2\Bigr].
\end{split}
\end{equation}

\end{document}

Answer 2

You should also have a look at the mathtime (mtpro2) fonts. The fonts are commercial, but one only has to pay for the full set, which most people don't need. The fonts are better in some ways (eg kerning) than some alternatives.