Does investing in the stock market contribute to economic growth? I am morally opposed to economic growth:  I think that for the good of our planet we need to be shrinking human impact in pretty much every way, not increasing it.
If I invest in the stock market, I am placing a bet that growth will continue for some time.  I think this is a reasonable bet to place, despite my opposition to it.
However, does my investment actually contribute to economic growth?  In particular, could anyone give an analysis of the likely impacts of either

Debt elimination (ex: paying off mortgage early)
Keeping the money in a savings account.
Buying government bonds.
Buying index funds.

on economic growth?
tl;dr
Yes, investing into stock market has positive impact on growth. First, before going any further, investing into stocks is from an economic perspective just a form of saving. Consequently, following the literature this answer will be repeatedly referring to saving in general.
In economics, there are two main theories of economic growth. An exogenous Solow-Swan growth theory and endogenous (eg Romer model) - see Romer Advanced Macroeconomics Ch 1-3. In both of these strands of literaterature saving impacts economic growth positively but under Solow-Swan increase in saving rate causes level increase in economic output which will show up as higher economic growth but in order to raise economic growth permanently a one would have to continuously increase. On the other hand under endogenous growth models increase in savings rate can have permanent positive effect on economic growth.
Effects of Savings Under Exogenous Growth
To illustrate the mechanisms at play consider augmented Mankiw-Weil-Romer (1992) Solow-Swan model given by:
$$ Y(t) = K(t)^{\alpha}H(t)^{\beta}(A(t)L(t))^{1-\alpha - \beta} \tag{1}$$
Where $Y$ is economic output (change of which is economic growth), and economic output varies positively $K$ is stock of capital, $H$ is stock of human capital (i.e. education) $A$ is the stock of technology (assumed to be growing at an exogenously given rate $(A (t) = A (0)e^{gt})$ and $L$ the stock of labor (growing at exogenously given rate $(L(t) = L (0)e^{nt})$. The Greek letters are exogenously given parameters that depend on the nature of society's production function (with $\alpha +\beta &lt;1$). Hence, when stock of capital, education, technology level or labor force expands economy will experience economic growth.
Now in order to see how savings plays a role in all this we can first define everything in terms of effective labor (e.g. $Y/AL= y$, $K/AL=k$ and $h/AL=h$), and using the fact that capital (and human capital as well) is determined by investment which is macroeconomically equivalent to saving we get that:
$$ \dot{k}(t) = s_k y(t) - (n + g + \delta_k)k(t), \tag{2}$$
$$ \dot{h}(t) = s_h y(t) - (n + g + \delta_h)h(t) \tag{3}$$
where $s_k$ is share of saving invested in physical capital and $s_h$ share of saving invested in education, whereas $\delta_k$ is depreciation of physical capital and $\delta_h$ erosion of human capital (e.g. loss skills over time). For simplicity it will be further assumed that $\delta_h = \delta_k=\delta$. Substituting the evolution of capital and human capital into the per capita version of (1) we get:
$$\ln y =  \ln A(0) + gt -  \frac{\alpha + \beta}{1-\alpha -\beta} \ln(n + g + \delta) +  \frac{\alpha }{1-\alpha -\beta} \ln s_k + \frac{ \beta}{1-\alpha -\beta} \ln s_h$$
Now stock market is stereotypically associated with investments into physical capital so I will focus mainly on relationship between output and physical capital. Hence, let us set growth rate of technology, population and to simplify calculation also depreciation to zero and let us assume technology stock and saving rate for human capital are fixed so their time derivates are zero. We end up with expression:
$$\ln y = \ln \bar{A} +  \frac{\alpha }{1-\alpha -\beta} \ln s_k + \frac{ \beta}{1-\alpha -\beta} \ln \bar{s_h} $$
Taking time derivative gives us:
$$ \frac{\dot{y}}{y} = \frac{\alpha }{1-\alpha -\beta} \frac{\dot{s_k}}{s_k}  $$
$\frac{\dot{y}}{y} $ is just continuous version of growth rate and consequently we can see that output growth depends on growth in savings rate. Furthermore, since $\alpha + \beta&lt;1$ the relationship will be strictly positive}.  However, a caveat here is that saving rate cannot growth forever as it has to be between $0\leq s \leq1$ since it is a proportion of income not consumed, so any increase in saving rate will increase the growth rate but you can only increase your saving rate to the point you devote your whole income to it. Visually a simulation of an increase in savings rate would produce the following result (see Romer Advanced Macroeconomics pp 20 - please note the simulation is based on simplified version of an above model so the precise shape of those curves might be different but the point carries over):

However, this being said  higher level of saving will still increase level of output which will lead to temporarily higher growth just the effect won't be permanent and the only thing that can permanently increase the per capita growth rate in exogenous growth rate model is an increase in rate of technological progress.
Effects of Savings Under Endogenous Growth
While the theory above is more widely accepted, recently this theory was expanded on by endogenous growth theory. I won't go into such deep detail into endogenous growth theory as models there get far more complicated, but I will try to explain in in relation to the exogenous growth model above.
In short, the gist of endogenous growth theory is that it rejects the exogenous growth theory assumption that technology develops at some exogenously given rate and society cannot do anything to speed up technological progress. Endogenous theory rejects that view and argues that investments in capital, education, or having larger labor force (and thus be able to devote more labor to R&amp;D projects) can increase the rate at which technology accumulates and so $g$ will be also function of investments into capital, education and share of labor devoted to R&amp;D (see discussion in Romer Advanced Macroeconomics Ch 3).
Now since you are interested primarily in saving via stock market the first relationship will be of greatest interest to you.  Now endogenous growth literature argues that the link between growth and saving here is mediated by either learning by doing it (e.g. investing money into building a cargo ship allows firms to learn how to better produce cargo ships - see Arrow, 1962). Next there will be link because firms can use portion of that investment to finance R&amp;D that then improves productivity of either capital or labor depending on what sort of production function industry has (e.g. see Romer 1990).
In economics there is still debate between the exogenous and endogenous growth camp, because given data we have it is very hard to statistically distinguish between endogenous and exogenous growth empirically (we have solid evidence for Solow-Swan model but it is difficult to distinguish transitory effect of saving from a permanent one with limited data), but recent Nobel Prize in Economics awarded to Romer in 2018 for his work on endogenous growth theory shows that this theory is becoming more dominant.
Summary
To sum it up, both major strands of economic literature shows saving whether through investment in stocks or in various other ways (putting your money in bank etc) has positive effect on economic growth. However, under exogenous growth theory this effect is just transitory whereas under endogenous growth theory there might be long lasting effect.
However, given that the economic literature on endogenous growth suggest that the link between saving and economic growth is mediated via investments in R&amp;D and learning by doing, if you want to minimize economic growth of society you can do your research and invest exclusively into stocks of companies that devote as little of their budget to new research as possible. This won't avoid effect due to learning by doing but it would almost certainly result in lower long term economic growth than investing into stock of companies that invest heavily into research.